Algebra Examples

$x - 3 y = 13$ $5 x + 6 z = 41$ $2 x + 4 y - z = 5$

Step 1

Add $3 y$ to both sides of the equation.

$x = 13 + 3 y$

$5 x + 6 z = 41$

$2 x + 4 y - z = 5$

Step 2

Replace all occurrences of $x$ with $13 + 3 y$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $5 x + 6 z = 41$ with $13 + 3 y$ .

$5 (13 + 3 y) + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$5 \cdot 13 + 5 (3 y) + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

Step 2.2.1.2

Multiply $5$ by $13$ .

$65 + 5 (3 y) + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

Step 2.2.1.3

Multiply $3$ by $5$ .

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$2 x + 4 y - z = 5$

Step 2.3

Replace all occurrences of $x$ in $2 x + 4 y - z = 5$ with $13 + 3 y$ .

$2 (13 + 3 y) + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $2 (13 + 3 y) + 4 y - z$ .

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.

$2 \cdot 13 + 2 (3 y) + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

Step 2.4.1.1.2

Multiply $2$ by $13$ .

$26 + 2 (3 y) + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

Step 2.4.1.1.3

Multiply $3$ by $2$ .

$26 + 6 y + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$26 + 6 y + 4 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

Step 2.4.1.2

Add $6 y$ and $4 y$ .

$26 + 10 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$26 + 10 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$26 + 10 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

$26 + 10 y - z = 5$

$65 + 15 y + 6 z = 41$

$x = 13 + 3 y$

Step 3

Reorder $13$ and $3 y$ .

$x = 3 y + 13$

$26 + 10 y - z = 5$

$65 + 15 y + 6 z = 41$

Step 4

Solve for $y$ in $26 + 10 y - z = 5$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $26$ from both sides of the equation.

$10 y - z = 5 - 26$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.1.2

Add $z$ to both sides of the equation.

$10 y = 5 - 26 + z$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.1.3

Subtract $26$ from $5$ .

$10 y = - 21 + z$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$10 y = - 21 + z$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.2

Divide each term in $10 y = - 21 + z$ by $10$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $10 y = - 21 + z$ by $10$ .

$\frac{10 y}{10} = \frac{- 21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$y = \frac{- 21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$y = \frac{- 21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Move the negative in front of the fraction.

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 3 y + 13$

$65 + 15 y + 6 z = 41$

Step 5

Replace all occurrences of $y$ with $- \frac{21}{10} + \frac{z}{10}$ in each equation.

Tap for more steps...

Step 5.1

Replace all occurrences of $y$ in $x = 3 y + 13$ with $- \frac{21}{10} + \frac{z}{10}$ .

$x = 3 (- \frac{21}{10} + \frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $3 (- \frac{21}{10} + \frac{z}{10}) + 13$ .

Tap for more steps...

Step 5.2.1.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1.1

Apply the distributive property.

$x = 3 (- \frac{21}{10}) + 3 (\frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.1.2

Multiply $3 (- \frac{21}{10})$ .

Tap for more steps...

Step 5.2.1.1.2.1

Multiply $- 1$ by $3$ .

$x = - 3 (\frac{21}{10}) + 3 (\frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.1.2.2

Combine $- 3$ and $\frac{21}{10}$ .

$x = \frac{- 3 \cdot 21}{10} + 3 (\frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.1.2.3

Multiply $- 3$ by $21$ .

$x = \frac{- 63}{10} + 3 (\frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

$x = \frac{- 63}{10} + 3 (\frac{z}{10}) + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.1.3

Combine $3$ and $\frac{z}{10}$ .

$x = \frac{- 63}{10} + \frac{3 z}{10} + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.1.4

Move the negative in front of the fraction.

$x = - \frac{63}{10} + \frac{3 z}{10} + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

$x = - \frac{63}{10} + \frac{3 z}{10} + 13$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.2

To write $13$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$x = \frac{3 z}{10} - \frac{63}{10} + 13 \cdot \frac{10}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.3

Combine $13$ and $\frac{10}{10}$ .

$x = \frac{3 z}{10} - \frac{63}{10} + \frac{13 \cdot 10}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.4

Combine the numerators over the common denominator.

$x = \frac{3 z}{10} + \frac{- 63 + 13 \cdot 10}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.5

Simplify the numerator.

Tap for more steps...

Step 5.2.1.5.1

Multiply $13$ by $10$ .

$x = \frac{3 z}{10} + \frac{- 63 + 130}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.2.1.5.2

Add $- 63$ and $130$ .

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 15 y + 6 z = 41$

Step 5.3

Replace all occurrences of $y$ in $65 + 15 y + 6 z = 41$ with $- \frac{21}{10} + \frac{z}{10}$ .

$65 + 15 (- \frac{21}{10} + \frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4

Simplify the left side.

Tap for more steps...

Step 5.4.1

Simplify $65 + 15 (- \frac{21}{10} + \frac{z}{10}) + 6 z$ .

Tap for more steps...

Step 5.4.1.1

Simplify each term.

Tap for more steps...

Step 5.4.1.1.1

Apply the distributive property.

$65 + 15 (- \frac{21}{10}) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.4.1.1.2.1

Move the leading negative in $- \frac{21}{10}$ into the numerator.

$65 + 15 (\frac{- 21}{10}) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.2.2

Factor $5$ out of $15$ .

$65 + 5 (3) (\frac{- 21}{10}) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.2.3

Factor $5$ out of $10$ .

$65 + 5 \cdot (3 (\frac{- 21}{5 \cdot 2})) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.2.4

Cancel the common factor.

$65 + 5 \cdot (3 (\frac{- 21}{5 \cdot 2})) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.2.5

Rewrite the expression.

$65 + 3 (\frac{- 21}{2}) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + 3 (\frac{- 21}{2}) + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.3

Combine $3$ and $\frac{- 21}{2}$ .

$65 + \frac{3 \cdot - 21}{2} + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.4

Multiply $3$ by $- 21$ .

$65 + \frac{- 63}{2} + 15 (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.5

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.4.1.1.5.1

Factor $5$ out of $15$ .

$65 + \frac{- 63}{2} + 5 (3) (\frac{z}{10}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.5.2

Factor $5$ out of $10$ .

$65 + \frac{- 63}{2} + 5 \cdot (3 (\frac{z}{5 \cdot 2})) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.5.3

Cancel the common factor.

$65 + \frac{- 63}{2} + 5 \cdot (3 (\frac{z}{5 \cdot 2})) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.5.4

Rewrite the expression.

$65 + \frac{- 63}{2} + 3 (\frac{z}{2}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 + \frac{- 63}{2} + 3 (\frac{z}{2}) + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.6

Combine $3$ and $\frac{z}{2}$ .

$65 + \frac{- 63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.1.7

Move the negative in front of the fraction.

$65 - \frac{63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$65 - \frac{63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.2

To write $65$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$65 \cdot \frac{2}{2} - \frac{63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.3

Combine $65$ and $\frac{2}{2}$ .

$\frac{65 \cdot 2}{2} - \frac{63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.4

Combine the numerators over the common denominator.

$\frac{65 \cdot 2 - 63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.5

Simplify the numerator.

Tap for more steps...

Step 5.4.1.5.1

Multiply $65$ by $2$ .

$\frac{130 - 63}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.5.2

Subtract $63$ from $130$ .

$\frac{67}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$\frac{67}{2} + \frac{3 z}{2} + 6 z = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.6

To write $6 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{67}{2} + \frac{3 z}{2} + 6 z \cdot \frac{2}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.7

Combine $6 z$ and $\frac{2}{2}$ .

$\frac{67}{2} + \frac{3 z}{2} + \frac{6 z \cdot 2}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.8

Combine the numerators over the common denominator.

$\frac{67}{2} + \frac{3 z + 6 z \cdot 2}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.9

Combine the numerators over the common denominator.

$\frac{67 + 3 z + 6 z \cdot 2}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.10

Multiply $2$ by $6$ .

$\frac{67 + 3 z + 12 z}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 5.4.1.11

Add $3 z$ and $12 z$ .

$\frac{67 + 15 z}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$\frac{67 + 15 z}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$\frac{67 + 15 z}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$\frac{67 + 15 z}{2} = 41$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6

Solve for $z$ in $\frac{67 + 15 z}{2} = 41$ .

Tap for more steps...

Step 6.1

Multiply both sides by $2$ .

$\frac{67 + 15 z}{2} \cdot 2 = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.2

Simplify.

Tap for more steps...

Step 6.2.1

Simplify the left side.

Tap for more steps...

Step 6.2.1.1

Simplify $\frac{67 + 15 z}{2} \cdot 2$ .

Tap for more steps...

Step 6.2.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1.1.1.1

Cancel the common factor.

$\frac{67 + 15 z}{2} \cdot 2 = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.2.1.1.1.2

Rewrite the expression.

$67 + 15 z = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$67 + 15 z = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.2.1.1.2

Reorder $67$ and $15 z$ .

$15 z + 67 = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$15 z + 67 = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$15 z + 67 = 41 \cdot 2$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.2.2

Simplify the right side.

Tap for more steps...

Step 6.2.2.1

Multiply $41$ by $2$ .

$15 z + 67 = 82$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$15 z + 67 = 82$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$15 z + 67 = 82$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3

Solve for $z$ .

Tap for more steps...

Step 6.3.1

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

Tap for more steps...

Step 6.3.1.1

Subtract $67$ from both sides of the equation.

$15 z = 82 - 67$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3.1.2

Subtract $67$ from $82$ .

$15 z = 15$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$15 z = 15$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3.2

Divide each term in $15 z = 15$ by $15$ and simplify.

Tap for more steps...

Step 6.3.2.1

Divide each term in $15 z = 15$ by $15$ .

$\frac{15 z}{15} = \frac{15}{15}$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3.2.2

Simplify the left side.

Tap for more steps...

Step 6.3.2.2.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 6.3.2.2.1.1

Cancel the common factor.

$\frac{15 z}{15} = \frac{15}{15}$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{15}{15}$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = \frac{15}{15}$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = \frac{15}{15}$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 6.3.2.3

Simplify the right side.

Tap for more steps...

Step 6.3.2.3.1

Divide $15$ by $15$ .

$z = 1$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = 1$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = 1$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = 1$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

$z = 1$

$x = \frac{3 z}{10} + \frac{67}{10}$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7

Replace all occurrences of $z$ with $1$ in each equation.

Tap for more steps...

Step 7.1

Replace all occurrences of $z$ in $x = \frac{3 z}{10} + \frac{67}{10}$ with $1$ .

$x = \frac{3 (1)}{10} + \frac{67}{10}$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7.2

Simplify the right side.

Tap for more steps...

Step 7.2.1

Simplify $\frac{3 (1)}{10} + \frac{67}{10}$ .

Tap for more steps...

Step 7.2.1.1

Combine the numerators over the common denominator.

$x = \frac{3 (1) + 67}{10}$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7.2.1.2

Simplify the expression.

Tap for more steps...

Step 7.2.1.2.1

Multiply $3$ by $1$ .

$x = \frac{3 + 67}{10}$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7.2.1.2.2

Add $3$ and $67$ .

$x = \frac{70}{10}$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7.2.1.2.3

Divide $70$ by $10$ .

$x = 7$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 7$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 7$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

$x = 7$

$z = 1$

$y = - \frac{21}{10} + \frac{z}{10}$

Step 7.3

Replace all occurrences of $z$ in $y = - \frac{21}{10} + \frac{z}{10}$ with $1$ .

$y = - \frac{21}{10} + \frac{1}{10}$

$x = 7$

$z = 1$

Step 7.4

Simplify the right side.

Tap for more steps...

Step 7.4.1

Simplify $- \frac{21}{10} + \frac{1}{10}$ .

Tap for more steps...

Step 7.4.1.1

Combine the numerators over the common denominator.

$y = \frac{- 21 + 1}{10}$

$x = 7$

$z = 1$

Step 7.4.1.2

Simplify the expression.

Tap for more steps...

Step 7.4.1.2.1

Add $- 21$ and $1$ .

$y = \frac{- 20}{10}$

$x = 7$

$z = 1$

Step 7.4.1.2.2

Divide $- 20$ by $10$ .

$y = - 2$

$x = 7$

$z = 1$

$y = - 2$

$x = 7$

$z = 1$

$y = - 2$

$x = 7$

$z = 1$

$y = - 2$

$x = 7$

$z = 1$

$y = - 2$

$x = 7$

$z = 1$

Step 8

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

$(7, - 2, 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(7, - 2, 1)$

Equation Form:

$x = 7, y = - 2, z = 1$