Algebra Examples

$- 6 x - 2 y + 2 z = - 8$ $3 x - 2 y - 4 z = 8$ $6 x - 2 y - 6 z = - 18$

Step 1

Solve for $x$ in $- 6 x - 2 y + 2 z = - 8$ .

Tap for more steps...

Step 1.1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 1.1.1

Add $2 y$ to both sides of the equation.

$- 6 x + 2 z = - 8 + 2 y$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.1.2

Subtract $2 z$ from both sides of the equation.

$- 6 x = - 8 + 2 y - 2 z$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$- 6 x = - 8 + 2 y - 2 z$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2

Divide each term in $- 6 x = - 8 + 2 y - 2 z$ by $- 6$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 6 x = - 8 + 2 y - 2 z$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 8}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 8}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{- 8}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{- 8}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Cancel the common factor of $- 8$ and $- 6$ .

Tap for more steps...

Step 1.2.3.1.1.1

Factor $- 2$ out of $- 8$ .

$x = \frac{- 2 \cdot 4}{- 6} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.1.2.1

Factor $- 2$ out of $- 6$ .

$x = \frac{- 2 \cdot 4}{- 2 \cdot 3} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 4}{- 2 \cdot 3} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{4}{3} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} + \frac{2 y}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.2

Cancel the common factor of $2$ and $- 6$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $2$ out of $2 y$ .

$x = \frac{4}{3} + \frac{2 (y)}{- 6} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.2.1

Factor $2$ out of $- 6$ .

$x = \frac{4}{3} + \frac{2 y}{2 \cdot - 3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = \frac{4}{3} + \frac{2 y}{2 \cdot - 3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = \frac{4}{3} + \frac{y}{- 3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} + \frac{y}{- 3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} + \frac{y}{- 3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = \frac{4}{3} - \frac{y}{3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.4

Cancel the common factor of $- 2$ and $- 6$ .

Tap for more steps...

Step 1.2.3.1.4.1

Factor $- 2$ out of $- 2 z$ .

$x = \frac{4}{3} - \frac{y}{3} + \frac{- 2 z}{- 6}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.4.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.4.2.1

Factor $- 2$ out of $- 6$ .

$x = \frac{4}{3} - \frac{y}{3} + \frac{- 2 z}{- 2 \cdot 3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.4.2.2

Cancel the common factor.

$x = \frac{4}{3} - \frac{y}{3} + \frac{- 2 z}{- 2 \cdot 3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 1.2.3.1.4.2.3

Rewrite the expression.

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$3 x - 2 y - 4 z = 8$

$6 x - 2 y - 6 z = - 18$

Step 2

Replace all occurrences of $x$ with $\frac{4}{3} - \frac{y}{3} + \frac{z}{3}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $3 x - 2 y - 4 z = 8$ with $\frac{4}{3} - \frac{y}{3} + \frac{z}{3}$ .

$3 (\frac{4}{3} - \frac{y}{3} + \frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $3 (\frac{4}{3} - \frac{y}{3} + \frac{z}{3}) - 2 y - 4 z$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$3 (\frac{4}{3}) + 3 (- \frac{y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.2.1.1

Cancel the common factor.

$3 (\frac{4}{3}) + 3 (- \frac{y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.1.2

Rewrite the expression.

$4 + 3 (- \frac{y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 + 3 (- \frac{y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.2.2.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$4 + 3 (\frac{- y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.2.2

Cancel the common factor.

$4 + 3 (\frac{- y}{3}) + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.2.3

Rewrite the expression.

$4 - y + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - y + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.2.3.1

Cancel the common factor.

$4 - y + 3 (\frac{z}{3}) - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.1.2.3.2

Rewrite the expression.

$4 - y + z - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - y + z - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - y + z - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - y + z - 2 y - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1.2.1

Subtract $2 y$ from $- y$ .

$4 - 3 y + z - 4 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.2.1.2.2

Subtract $4 z$ from $z$ .

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$6 x - 2 y - 6 z = - 18$

Step 2.3

Replace all occurrences of $x$ in $6 x - 2 y - 6 z = - 18$ with $\frac{4}{3} - \frac{y}{3} + \frac{z}{3}$ .

$6 (\frac{4}{3} - \frac{y}{3} + \frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $6 (\frac{4}{3} - \frac{y}{3} + \frac{z}{3}) - 2 y - 6 z$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$6 (\frac{4}{3}) + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1.1.2.1.1

Factor $3$ out of $6$ .

$3 (2) (\frac{4}{3}) + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.1.2

Cancel the common factor.

$3 \cdot (2 (\frac{4}{3})) + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.1.3

Rewrite the expression.

$2 \cdot 4 + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$2 \cdot 4 + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.2

Multiply $2$ by $4$ .

$8 + 6 (- \frac{y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1.1.2.3.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$8 + 6 (\frac{- y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.3.2

Factor $3$ out of $6$ .

$8 + 3 (2) (\frac{- y}{3}) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.3.3

Cancel the common factor.

$8 + 3 \cdot (2 (\frac{- y}{3})) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.3.4

Rewrite the expression.

$8 + 2 (- y) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 + 2 (- y) + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.4

Multiply $- 1$ by $2$ .

$8 - 2 y + 6 (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1.1.2.5.1

Factor $3$ out of $6$ .

$8 - 2 y + 3 (2) (\frac{z}{3}) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.5.2

Cancel the common factor.

$8 - 2 y + 3 \cdot (2 (\frac{z}{3})) - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.1.2.5.3

Rewrite the expression.

$8 - 2 y + 2 z - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 2 y + 2 z - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 2 y + 2 z - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 2 y + 2 z - 2 y - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.4.1.2.1

Subtract $2 y$ from $- 2 y$ .

$8 - 4 y + 2 z - 6 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 2.4.1.2.2

Subtract $6 z$ from $2 z$ .

$8 - 4 y - 4 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 4 y - 4 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 4 y - 4 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 4 y - 4 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$8 - 4 y - 4 z = - 18$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3

Solve for $y$ in $8 - 4 y - 4 z = - 18$ .

Tap for more steps...

Step 3.1

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $8$ from both sides of the equation.

$- 4 y - 4 z = - 18 - 8$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.1.2

Add $4 z$ to both sides of the equation.

$- 4 y = - 18 - 8 + 4 z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.1.3

Subtract $8$ from $- 18$ .

$- 4 y = - 26 + 4 z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$- 4 y = - 26 + 4 z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2

Divide each term in $- 4 y = - 26 + 4 z$ by $- 4$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 4 y = - 26 + 4 z$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 26}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 26}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 26}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{- 26}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{- 26}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

Cancel the common factor of $- 26$ and $- 4$ .

Tap for more steps...

Step 3.2.3.1.1.1

Factor $- 2$ out of $- 26$ .

$y = \frac{- 2 \cdot 13}{- 4} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 3.2.3.1.1.2.1

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 13}{- 2 \cdot 2} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 2 \cdot 13}{- 2 \cdot 2} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{13}{2} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} + \frac{4 z}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.2

Cancel the common factor of $4$ and $- 4$ .

Tap for more steps...

Step 3.2.3.1.2.1

Factor $4$ out of $4 z$ .

$y = \frac{13}{2} + \frac{4 (z)}{- 4}$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.2.2

Move the negative one from the denominator of $\frac{z}{- 1}$ .

$y = \frac{13}{2} - 1 \cdot z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} - 1 \cdot z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 3.2.3.1.3

Rewrite $- 1 \cdot z$ as $- z$ .

$y = \frac{13}{2} - z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} - z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} - z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} - z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$y = \frac{13}{2} - z$

$4 - 3 y - 3 z = 8$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4

Replace all occurrences of $y$ with $\frac{13}{2} - z$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $4 - 3 y - 3 z = 8$ with $\frac{13}{2} - z$ .

$4 - 3 (\frac{13}{2} - z) - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $4 - 3 (\frac{13}{2} - z) - 3 z$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Apply the distributive property.

$4 - 3 (\frac{13}{2}) - 3 (- z) - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.1.2

Multiply $- 3 (\frac{13}{2})$ .

Tap for more steps...

Step 4.2.1.1.2.1

Combine $- 3$ and $\frac{13}{2}$ .

$4 + \frac{- 3 \cdot 13}{2} - 3 (- z) - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.1.2.2

Multiply $- 3$ by $13$ .

$4 + \frac{- 39}{2} - 3 (- z) - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$4 + \frac{- 39}{2} - 3 (- z) - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.1.3

Multiply $- 1$ by $- 3$ .

$4 + \frac{- 39}{2} + 3 z - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.1.4

Move the negative in front of the fraction.

$4 - \frac{39}{2} + 3 z - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$4 - \frac{39}{2} + 3 z - 3 z = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.2

Combine the opposite terms in $4 - \frac{39}{2} + 3 z - 3 z$ .

Tap for more steps...

Step 4.2.1.2.1

Subtract $3 z$ from $3 z$ .

$4 - \frac{39}{2} + 0 = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.2.2

Add $4 - \frac{39}{2}$ and $0$ .

$4 - \frac{39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$4 - \frac{39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.3

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} - \frac{39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.4

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} - \frac{39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.5

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 - 39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.6

Simplify the numerator.

Tap for more steps...

Step 4.2.1.6.1

Multiply $4$ by $2$ .

$\frac{8 - 39}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.6.2

Subtract $39$ from $8$ .

$\frac{- 31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$\frac{- 31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.2.1.7

Move the negative in front of the fraction.

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$

Step 4.3

Replace all occurrences of $y$ in $x = \frac{4}{3} - \frac{y}{3} + \frac{z}{3}$ with $\frac{13}{2} - z$ .

$x = \frac{4}{3} - \frac{\frac{13}{2} - z}{3} + \frac{z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $\frac{4}{3} - \frac{\frac{13}{2} - z}{3} + \frac{z}{3}$ .

Tap for more steps...

Step 4.4.1.1

Combine the numerators over the common denominator.

$x = \frac{4 - (\frac{13}{2} - z) + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.2

Simplify each term.

Tap for more steps...

Step 4.4.1.2.1

Apply the distributive property.

$x = \frac{4 - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.2.2

Multiply $- - z$ .

Tap for more steps...

Step 4.4.1.2.2.1

Multiply $- 1$ by $- 1$ .

$x = \frac{4 - \frac{13}{2} + 1 z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.2.2.2

Multiply $z$ by $1$ .

$x = \frac{4 - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4 - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{4 - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.3

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{4 \cdot \frac{2}{2} - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.4

Combine $4$ and $\frac{2}{2}$ .

$x = \frac{\frac{4 \cdot 2}{2} - \frac{13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.5

Combine the numerators over the common denominator.

$x = \frac{\frac{4 \cdot 2 - 13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.6

Simplify the numerator.

Tap for more steps...

Step 4.4.1.6.1

Multiply $4$ by $2$ .

$x = \frac{\frac{8 - 13}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.6.2

Subtract $13$ from $8$ .

$x = \frac{\frac{- 5}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{\frac{- 5}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.7

Simplify by adding terms.

Tap for more steps...

Step 4.4.1.7.1

Move the negative in front of the fraction.

$x = \frac{- \frac{5}{2} + z + z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.7.2

Add $z$ and $z$ .

$x = \frac{- \frac{5}{2} + 2 z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{- \frac{5}{2} + 2 z}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.8

Simplify the numerator.

Tap for more steps...

Step 4.4.1.8.1

To write $2 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{- \frac{5}{2} + 2 z \cdot \frac{2}{2}}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.8.2

Combine $2 z$ and $\frac{2}{2}$ .

$x = \frac{- \frac{5}{2} + \frac{2 z \cdot 2}{2}}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.8.3

Combine the numerators over the common denominator.

$x = \frac{\frac{- 5 + 2 z \cdot 2}{2}}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.8.4

Multiply $2$ by $2$ .

$x = \frac{\frac{- 5 + 4 z}{2}}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{\frac{- 5 + 4 z}{2}}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.9

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{- 5 + 4 z}{2} \cdot \frac{1}{3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.10

Multiply $\frac{- 5 + 4 z}{2} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 4.4.1.10.1

Multiply $\frac{- 5 + 4 z}{2}$ by $\frac{1}{3}$ .

$x = \frac{- 5 + 4 z}{2 \cdot 3}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.10.2

Multiply $2$ by $3$ .

$x = \frac{- 5 + 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = \frac{- 5 + 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.11

Rewrite $- 5$ as $- 1 (5)$ .

$x = \frac{- 1 \cdot 5 + 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.12

Factor $- 1$ out of $4 z$ .

$x = \frac{- 1 \cdot 5 - (- 4 z)}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.13

Factor $- 1$ out of $- 1 (5) - (- 4 z)$ .

$x = \frac{- 1 (5 - 4 z)}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 4.4.1.14

Move the negative in front of the fraction.

$x = - \frac{5 - 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = - \frac{5 - 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = - \frac{5 - 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

$x = - \frac{5 - 4 z}{6}$

$- \frac{31}{2} = 8$

$y = \frac{13}{2} - z$

Step 5

Since $- \frac{31}{2} = 8$ is not true, there is no solution.

No solution