Algebra Examples

$3 x - y + z = 3$ $- x + y + 2 z = 0$ $- 5 x + 3 y + 2 z = - 2$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $3 x$ from both sides of the equation.

$- y + z = 3 - 3 x$

$- x + y + 2 z = 0$

$- 5 x + 3 y + 2 z = - 2$

Step 1.2

Add $y$ to both sides of the equation.

$z = 3 - 3 x + y$

$- x + y + 2 z = 0$

$- 5 x + 3 y + 2 z = - 2$

$z = 3 - 3 x + y$

$- x + y + 2 z = 0$

$- 5 x + 3 y + 2 z = - 2$

Step 2

Replace all occurrences of $z$ with $3 - 3 x + y$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $z$ in $- x + y + 2 z = 0$ with $3 - 3 x + y$ .

$- x + y + 2 (3 - 3 x + y) = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $- x + y + 2 (3 - 3 x + y)$ .

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.

$- x + y + 2 \cdot 3 + 2 (- 3 x) + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $2$ by $3$ .

$- x + y + 6 + 2 (- 3 x) + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.2.1.1.2.2

Multiply $- 3$ by $2$ .

$- x + y + 6 - 6 x + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

$- x + y + 6 - 6 x + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

$- x + y + 6 - 6 x + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1.2.1

Subtract $6 x$ from $- x$ .

$- 7 x + y + 6 + 2 y = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.2.1.2.2

Add $y$ and $2 y$ .

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 2 z = - 2$

Step 2.3

Replace all occurrences of $z$ in $- 5 x + 3 y + 2 z = - 2$ with $3 - 3 x + y$ .

$- 5 x + 3 y + 2 (3 - 3 x + y) = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $- 5 x + 3 y + 2 (3 - 3 x + y)$ .

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.

$- 5 x + 3 y + 2 \cdot 3 + 2 (- 3 x) + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Multiply $2$ by $3$ .

$- 5 x + 3 y + 6 + 2 (- 3 x) + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 2.4.1.1.2.2

Multiply $- 3$ by $2$ .

$- 5 x + 3 y + 6 - 6 x + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 6 - 6 x + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 5 x + 3 y + 6 - 6 x + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 2.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.4.1.2.1

Subtract $6 x$ from $- 5 x$ .

$- 11 x + 3 y + 6 + 2 y = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 2.4.1.2.2

Add $3 y$ and $2 y$ .

$- 11 x + 5 y + 6 = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 11 x + 5 y + 6 = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 11 x + 5 y + 6 = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 11 x + 5 y + 6 = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 11 x + 5 y + 6 = - 2$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3

Solve for $x$ in $- 11 x + 5 y + 6 = - 2$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $5 y$ from both sides of the equation.

$- 11 x + 6 = - 2 - 5 y$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.1.2

Subtract $6$ from both sides of the equation.

$- 11 x = - 2 - 5 y - 6$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.1.3

Subtract $6$ from $- 2$ .

$- 11 x = - 5 y - 8$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$- 11 x = - 5 y - 8$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.2

Divide each term in $- 11 x = - 5 y - 8$ by $- 11$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 11 x = - 5 y - 8$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 5 y}{- 11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 11$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 5 y}{- 11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5 y}{- 11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{- 5 y}{- 11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{- 5 y}{- 11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

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

Dividing two negative values results in a positive value.

$x = \frac{5 y}{11} + \frac{- 8}{- 11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$x = \frac{5 y}{11} + \frac{8}{11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{5 y}{11} + \frac{8}{11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{5 y}{11} + \frac{8}{11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{5 y}{11} + \frac{8}{11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

$x = \frac{5 y}{11} + \frac{8}{11}$

$- 7 x + 3 y + 6 = 0$

$z = 3 - 3 x + y$

Step 4

Replace all occurrences of $x$ with $\frac{5 y}{11} + \frac{8}{11}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $x$ in $- 7 x + 3 y + 6 = 0$ with $\frac{5 y}{11} + \frac{8}{11}$ .

$- 7 (\frac{5 y}{11} + \frac{8}{11}) + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $- 7 (\frac{5 y}{11} + \frac{8}{11}) + 3 y + 6$ .

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.

$- 7 \frac{5 y}{11} - 7 (\frac{8}{11}) + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.2

Multiply $- 7 \frac{5 y}{11}$ .

Tap for more steps...

Step 4.2.1.1.2.1

Combine $- 7$ and $\frac{5 y}{11}$ .

$\frac{- 7 (5 y)}{11} - 7 (\frac{8}{11}) + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.2.2

Multiply $5$ by $- 7$ .

$\frac{- 35 y}{11} - 7 (\frac{8}{11}) + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$\frac{- 35 y}{11} - 7 (\frac{8}{11}) + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.3

Multiply $- 7 (\frac{8}{11})$ .

Tap for more steps...

Step 4.2.1.1.3.1

Combine $- 7$ and $\frac{8}{11}$ .

$\frac{- 35 y}{11} + \frac{- 7 \cdot 8}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.3.2

Multiply $- 7$ by $8$ .

$\frac{- 35 y}{11} + \frac{- 56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$\frac{- 35 y}{11} + \frac{- 56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.4

Simplify each term.

Tap for more steps...

Step 4.2.1.1.4.1

Move the negative in front of the fraction.

$- \frac{35 y}{11} + \frac{- 56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.1.4.2

Move the negative in front of the fraction.

$- \frac{35 y}{11} - \frac{56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{35 y}{11} - \frac{56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{35 y}{11} - \frac{56}{11} + 3 y + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.2

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- \frac{35 y}{11} + 3 y \cdot \frac{11}{11} - \frac{56}{11} + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.3

Combine $3 y$ and $\frac{11}{11}$ .

$- \frac{35 y}{11} + \frac{3 y \cdot 11}{11} - \frac{56}{11} + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{- 35 y + 3 y \cdot 11}{11} - \frac{56}{11} + 6 = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.5

Combine the numerators over the common denominator.

$6 + \frac{- 35 y + 3 y \cdot 11 - 56}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.6

Multiply $11$ by $3$ .

$6 + \frac{- 35 y + 33 y - 56}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.7

Add $- 35 y$ and $33 y$ .

$6 + \frac{- 2 y - 56}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.8

Factor $2$ out of $- 2 y - 56$ .

Tap for more steps...

Step 4.2.1.8.1

Factor $2$ out of $- 2 y$ .

$6 + \frac{2 (- y) - 56}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.8.2

Factor $2$ out of $- 56$ .

$6 + \frac{2 (- y) + 2 (- 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.8.3

Factor $2$ out of $2 (- y) + 2 (- 28)$ .

$6 + \frac{2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$6 + \frac{2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.9

To write $6$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$6 \cdot \frac{11}{11} + \frac{2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.10

Simplify terms.

Tap for more steps...

Step 4.2.1.10.1

Combine $6$ and $\frac{11}{11}$ .

$\frac{6 \cdot 11}{11} + \frac{2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.10.2

Combine the numerators over the common denominator.

$\frac{6 \cdot 11 + 2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$\frac{6 \cdot 11 + 2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.11

Simplify the numerator.

Tap for more steps...

Step 4.2.1.11.1

Factor $2$ out of $6 \cdot 11 + 2 (- y - 28)$ .

Tap for more steps...

Step 4.2.1.11.1.1

Factor $2$ out of $6 \cdot 11$ .

$\frac{2 (3 \cdot 11) + 2 (- y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.11.1.2

Factor $2$ out of $2 (3 \cdot 11) + 2 (- y - 28)$ .

$\frac{2 (3 \cdot 11 - y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$\frac{2 (3 \cdot 11 - y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.11.2

Multiply $3$ by $11$ .

$\frac{2 (33 - y - 28)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.11.3

Subtract $28$ from $33$ .

$\frac{2 (- y + 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$\frac{2 (- y + 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.12

Simplify with factoring out.

Tap for more steps...

Step 4.2.1.12.1

Factor $- 1$ out of $- y$ .

$\frac{2 (- (y) + 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.12.2

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

$\frac{2 (- (y) - 1 \cdot - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.12.3

Factor $- 1$ out of $- (y) - 1 (- 5)$ .

$\frac{2 (- (y - 5))}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.12.4

Simplify the expression.

Tap for more steps...

Step 4.2.1.12.4.1

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

$\frac{2 (- 1 (y - 5))}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.2.1.12.4.2

Move the negative in front of the fraction.

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - 3 x + y$

Step 4.3

Replace all occurrences of $x$ in $z = 3 - 3 x + y$ with $\frac{5 y}{11} + \frac{8}{11}$ .

$z = 3 - 3 (\frac{5 y}{11} + \frac{8}{11}) + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $3 - 3 (\frac{5 y}{11} + \frac{8}{11}) + y$ .

Tap for more steps...

Step 4.4.1.1

Simplify each term.

Tap for more steps...

Step 4.4.1.1.1

Apply the distributive property.

$z = 3 - 3 \frac{5 y}{11} - 3 (\frac{8}{11}) + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.2

Multiply $- 3 \frac{5 y}{11}$ .

Tap for more steps...

Step 4.4.1.1.2.1

Combine $- 3$ and $\frac{5 y}{11}$ .

$z = 3 + \frac{- 3 (5 y)}{11} - 3 (\frac{8}{11}) + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.2.2

Multiply $5$ by $- 3$ .

$z = 3 + \frac{- 15 y}{11} - 3 (\frac{8}{11}) + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 + \frac{- 15 y}{11} - 3 (\frac{8}{11}) + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.3

Multiply $- 3 (\frac{8}{11})$ .

Tap for more steps...

Step 4.4.1.1.3.1

Combine $- 3$ and $\frac{8}{11}$ .

$z = 3 + \frac{- 15 y}{11} + \frac{- 3 \cdot 8}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.3.2

Multiply $- 3$ by $8$ .

$z = 3 + \frac{- 15 y}{11} + \frac{- 24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 + \frac{- 15 y}{11} + \frac{- 24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.4

Simplify each term.

Tap for more steps...

Step 4.4.1.1.4.1

Move the negative in front of the fraction.

$z = 3 - \frac{15 y}{11} + \frac{- 24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.1.4.2

Move the negative in front of the fraction.

$z = 3 - \frac{15 y}{11} - \frac{24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - \frac{15 y}{11} - \frac{24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = 3 - \frac{15 y}{11} - \frac{24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$z = - \frac{15 y}{11} + 3 \cdot \frac{11}{11} - \frac{24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.3

Combine $3$ and $\frac{11}{11}$ .

$z = - \frac{15 y}{11} + \frac{3 \cdot 11}{11} - \frac{24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$z = - \frac{15 y}{11} + \frac{3 \cdot 11 - 24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.5

Simplify the numerator.

Tap for more steps...

Step 4.4.1.5.1

Multiply $3$ by $11$ .

$z = - \frac{15 y}{11} + \frac{33 - 24}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.5.2

Subtract $24$ from $33$ .

$z = - \frac{15 y}{11} + \frac{9}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{15 y}{11} + \frac{9}{11} + y$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.6

To write $y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$z = - \frac{15 y}{11} + y \cdot \frac{11}{11} + \frac{9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.7

Simplify terms.

Tap for more steps...

Step 4.4.1.7.1

Combine $y$ and $\frac{11}{11}$ .

$z = - \frac{15 y}{11} + \frac{y \cdot 11}{11} + \frac{9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.7.2

Combine the numerators over the common denominator.

$z = \frac{- 15 y + y \cdot 11}{11} + \frac{9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.7.3

Combine the numerators over the common denominator.

$z = \frac{- 15 y + y \cdot 11 + 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = \frac{- 15 y + y \cdot 11 + 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.8

Move $11$ to the left of $y$ .

$z = \frac{- 15 y + 11 y + 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9

Simplify terms.

Tap for more steps...

Step 4.4.1.9.1

Add $- 15 y$ and $11 y$ .

$z = \frac{- 4 y + 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9.2

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

$z = \frac{- (4 y) + 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9.3

Rewrite $9$ as $- 1 (- 9)$ .

$z = \frac{- (4 y) - 1 \cdot - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9.4

Factor $- 1$ out of $- (4 y) - 1 (- 9)$ .

$z = \frac{- (4 y - 9)}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9.5

Simplify the expression.

Tap for more steps...

Step 4.4.1.9.5.1

Rewrite $- (4 y - 9)$ as $- 1 (4 y - 9)$ .

$z = \frac{- 1 (4 y - 9)}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 4.4.1.9.5.2

Move the negative in front of the fraction.

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{4 y - 9}{11}$

$- \frac{2 (y - 5)}{11} = 0$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5

Solve for $y$ in $- \frac{2 (y - 5)}{11} = 0$ .

Tap for more steps...

Step 5.1

Set the numerator equal to zero.

$2 (y - 5) = 0$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5.2

Solve the equation for $y$ .

Tap for more steps...

Step 5.2.1

Divide each term in $2 (y - 5) = 0$ by $2$ and simplify.

Tap for more steps...

Step 5.2.1.1

Divide each term in $2 (y - 5) = 0$ by $2$ .

$\frac{2 (y - 5)}{2} = \frac{0}{2}$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5.2.1.2

Simplify the left side.

Tap for more steps...

Step 5.2.1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.2.1.1

Cancel the common factor.

$\frac{2 (y - 5)}{2} = \frac{0}{2}$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5.2.1.2.1.2

Divide $y - 5$ by $1$ .

$y - 5 = \frac{0}{2}$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y - 5 = \frac{0}{2}$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y - 5 = \frac{0}{2}$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5.2.1.3

Simplify the right side.

Tap for more steps...

Step 5.2.1.3.1

Divide $0$ by $2$ .

$y - 5 = 0$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y - 5 = 0$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y - 5 = 0$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 5.2.2

Add $5$ to both sides of the equation.

$y = 5$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y = 5$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

$y = 5$

$z = - \frac{4 y - 9}{11}$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6

Replace all occurrences of $y$ with $5$ in each equation.

Tap for more steps...

Step 6.1

Replace all occurrences of $y$ in $z = - \frac{4 y - 9}{11}$ with $5$ .

$z = - \frac{4 (5) - 9}{11}$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- \frac{4 (5) - 9}{11}$ .

Tap for more steps...

Step 6.2.1.1

Simplify the numerator.

Tap for more steps...

Step 6.2.1.1.1

Multiply $4$ by $5$ .

$z = - \frac{20 - 9}{11}$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.2.1.1.2

Subtract $9$ from $20$ .

$z = - \frac{11}{11}$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - \frac{11}{11}$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.2.1.2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.2.1.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 6.2.1.2.1.1

Cancel the common factor.

$z = - \frac{11}{11}$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.2.1.2.1.2

Rewrite the expression.

$z = - 1 \cdot 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - 1 \cdot 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.2.1.2.2

Multiply $- 1$ by $1$ .

$z = - 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

$z = - 1$

$y = 5$

$x = \frac{5 y}{11} + \frac{8}{11}$

Step 6.3

Replace all occurrences of $y$ in $x = \frac{5 y}{11} + \frac{8}{11}$ with $5$ .

$x = \frac{5 (5)}{11} + \frac{8}{11}$

$z = - 1$

$y = 5$

Step 6.4

Simplify the right side.

Tap for more steps...

Step 6.4.1

Simplify $\frac{5 (5)}{11} + \frac{8}{11}$ .

Tap for more steps...

Step 6.4.1.1

Combine the numerators over the common denominator.

$x = \frac{5 (5) + 8}{11}$

$z = - 1$

$y = 5$

Step 6.4.1.2

Simplify the expression.

Tap for more steps...

Step 6.4.1.2.1

Multiply $5$ by $5$ .

$x = \frac{25 + 8}{11}$

$z = - 1$

$y = 5$

Step 6.4.1.2.2

Add $25$ and $8$ .

$x = \frac{33}{11}$

$z = - 1$

$y = 5$

Step 6.4.1.2.3

Divide $33$ by $11$ .

$x = 3$

$z = - 1$

$y = 5$

$x = 3$

$z = - 1$

$y = 5$

$x = 3$

$z = - 1$

$y = 5$

$x = 3$

$z = - 1$

$y = 5$

$x = 3$

$z = - 1$

$y = 5$

Step 7

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(3, 5, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(3, 5, - 1)$

Equation Form:

$x = 3, y = 5, z = - 1$