Solve by Substitution 4x-2y-z=-5 , x-3y+2z=3 , 3x+y-2z=-5

$4 x - 2 y - z = - 5$ , $x - 3 y + 2 z = 3$ , $3 x + y - 2 z = - 5$

Step 1

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

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

$x + 2 z = 3 + 3 y$

$4 x - 2 y - z = - 5$

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

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

$x = 3 + 3 y - 2 z$

$4 x - 2 y - z = - 5$

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

$x = 3 + 3 y - 2 z$

$4 x - 2 y - z = - 5$

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

Step 2

Replace all occurrences of $x$ with $3 + 3 y - 2 z$ in each equation.

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

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

$x = 3 + 3 y - 2 z$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = 3 + 3 y - 2 z$

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

Simplify.

Multiply $4$ by $3$ .

$12 + 4 (3 y) + 4 (- 2 z) - 2 y - z = - 5$

$x = 3 + 3 y - 2 z$

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

Multiply $3$ by $4$ .

$12 + 12 y + 4 (- 2 z) - 2 y - z = - 5$

$x = 3 + 3 y - 2 z$

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

Multiply $- 2$ by $4$ .

$12 + 12 y - 8 z - 2 y - z = - 5$

$x = 3 + 3 y - 2 z$

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

$12 + 12 y - 8 z - 2 y - z = - 5$

$x = 3 + 3 y - 2 z$

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

$12 + 12 y - 8 z - 2 y - z = - 5$

$x = 3 + 3 y - 2 z$

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

Simplify by adding terms.

Subtract $2 y$ from $12 y$ .

$12 + 10 y - 8 z - z = - 5$

$x = 3 + 3 y - 2 z$

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

Subtract $z$ from $- 8 z$ .

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

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

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

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

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

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

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

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

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

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

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Simplify.

Multiply $3$ by $3$ .

$9 + 3 (3 y) + 3 (- 2 z) + y - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Multiply $3$ by $3$ .

$9 + 9 y + 3 (- 2 z) + y - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Multiply $- 2$ by $3$ .

$9 + 9 y - 6 z + y - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 9 y - 6 z + y - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 9 y - 6 z + y - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Simplify by adding terms.

Add $9 y$ and $y$ .

$9 + 10 y - 6 z - 2 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Subtract $2 z$ from $- 6 z$ .

$9 + 10 y - 8 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 10 y - 8 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 10 y - 8 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 10 y - 8 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$9 + 10 y - 8 z = - 5$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Step 3

Solve for $y$ in $9 + 10 y - 8 z = - 5$ .

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

Subtract $9$ from both sides of the equation.

$10 y - 8 z = - 5 - 9$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Add $8 z$ to both sides of the equation.

$10 y = - 5 - 9 + 8 z$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Subtract $9$ from $- 5$ .

$10 y = - 14 + 8 z$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$10 y = - 14 + 8 z$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Divide each term in $10 y = - 14 + 8 z$ by $10$ and simplify.

Divide each term in $10 y = - 14 + 8 z$ by $10$ .

$\frac{10 y}{10} = \frac{- 14}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 14}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Divide $y$ by $1$ .

$y = \frac{- 14}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = \frac{- 14}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = \frac{- 14}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 14$ and $10$ .

Factor $2$ out of $- 14$ .

$y = \frac{2 (- 7)}{10} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Cancel the common factors.

Factor $2$ out of $10$ .

$y = \frac{2 \cdot - 7}{2 \cdot 5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Cancel the common factor.

$y = \frac{2 \cdot - 7}{2 \cdot 5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Rewrite the expression.

$y = \frac{- 7}{5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = \frac{- 7}{5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = \frac{- 7}{5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Move the negative in front of the fraction.

$y = - \frac{7}{5} + \frac{8 z}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Cancel the common factor of $8$ and $10$ .

Factor $2$ out of $8 z$ .

$y = - \frac{7}{5} + \frac{2 (4 z)}{10}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Cancel the common factors.

Factor $2$ out of $10$ .

$y = - \frac{7}{5} + \frac{2 (4 z)}{2 (5)}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Cancel the common factor.

$y = - \frac{7}{5} + \frac{2 (4 z)}{2 \cdot 5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Rewrite the expression.

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$12 + 10 y - 9 z = - 5$

$x = 3 + 3 y - 2 z$

Step 4

Replace all occurrences of $y$ with $- \frac{7}{5} + \frac{4 z}{5}$ in each equation.

Replace all occurrences of $y$ in $12 + 10 y - 9 z = - 5$ with $- \frac{7}{5} + \frac{4 z}{5}$ .

$12 + 10 (- \frac{7}{5} + \frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Simplify the left side.

Simplify $12 + 10 (- \frac{7}{5} + \frac{4 z}{5}) - 9 z$ .

Simplify each term.

Apply the distributive property.

$12 + 10 (- \frac{7}{5}) + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$12 + 10 (\frac{- 7}{5}) + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Factor $5$ out of $10$ .

$12 + 5 (2) (\frac{- 7}{5}) + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Cancel the common factor.

$12 + 5 \cdot (2 (\frac{- 7}{5})) + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Rewrite the expression.

$12 + 2 \cdot - 7 + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$12 + 2 \cdot - 7 + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Multiply $2$ by $- 7$ .

$12 - 14 + 10 (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$12 - 14 + 5 (2) (\frac{4 z}{5}) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Cancel the common factor.

$12 - 14 + 5 \cdot (2 (\frac{4 z}{5})) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Rewrite the expression.

$12 - 14 + 2 (4 z) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$12 - 14 + 2 (4 z) - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Multiply $4$ by $2$ .

$12 - 14 + 8 z - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$12 - 14 + 8 z - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Simplify by adding terms.

Subtract $14$ from $12$ .

$- 2 + 8 z - 9 z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Subtract $9 z$ from $8 z$ .

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + 3 y - 2 z$

Replace all occurrences of $y$ in $x = 3 + 3 y - 2 z$ with $- \frac{7}{5} + \frac{4 z}{5}$ .

$x = 3 + 3 (- \frac{7}{5} + \frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the right side.

Simplify $3 + 3 (- \frac{7}{5} + \frac{4 z}{5}) - 2 z$ .

Simplify each term.

Apply the distributive property.

$x = 3 + 3 (- \frac{7}{5}) + 3 (\frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $3 (- \frac{7}{5})$ .

Multiply $- 1$ by $3$ .

$x = 3 - 3 (\frac{7}{5}) + 3 (\frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine $- 3$ and $\frac{7}{5}$ .

$x = 3 + \frac{- 3 \cdot 7}{5} + 3 (\frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $- 3$ by $7$ .

$x = 3 + \frac{- 21}{5} + 3 (\frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + \frac{- 21}{5} + 3 (\frac{4 z}{5}) - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $3 \frac{4 z}{5}$ .

Combine $3$ and $\frac{4 z}{5}$ .

$x = 3 + \frac{- 21}{5} + \frac{3 (4 z)}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $4$ by $3$ .

$x = 3 + \frac{- 21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 + \frac{- 21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Move the negative in front of the fraction.

$x = 3 - \frac{21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 3 - \frac{21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = 3 \cdot \frac{5}{5} - \frac{21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine $3$ and $\frac{5}{5}$ .

$x = \frac{3 \cdot 5}{5} - \frac{21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine the numerators over the common denominator.

$x = \frac{3 \cdot 5 - 21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$x = \frac{15 - 21}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Subtract $21$ from $15$ .

$x = \frac{- 6}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = \frac{- 6}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Move the negative in front of the fraction.

$x = - \frac{6}{5} + \frac{12 z}{5} - 2 z$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

To write $- 2 z$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{6}{5} + \frac{12 z}{5} - 2 z \cdot \frac{5}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine $- 2 z$ and $\frac{5}{5}$ .

$x = - \frac{6}{5} + \frac{12 z}{5} + \frac{- 2 z \cdot 5}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine the numerators over the common denominator.

$x = - \frac{6}{5} + \frac{12 z - 2 z \cdot 5}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 6 + 12 z - 2 z \cdot 5}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $5$ by $- 2$ .

$x = \frac{- 6 + 12 z - 10 z}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Subtract $10 z$ from $12 z$ .

$x = \frac{- 6 + 2 z}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

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

Factor $2$ out of $- 6$ .

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Factor $2$ out of $2 \cdot - 3 + 2 z$ .

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Rewrite $- 3$ as $- 1 (3)$ .

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Factor $- 1$ out of $z$ .

$x = \frac{2 (- 1 \cdot 3 - 1 (- z))}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Factor $- 1$ out of $- 1 (3) - 1 (- z)$ .

$x = \frac{2 (- 1 (3 - z))}{5}$

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Move the negative in front of the fraction.

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

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

$- 2 - z = - 5$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Step 5

Solve for $z$ in $- 2 - z = - 5$ .

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

Add $2$ to both sides of the equation.

$- z = - 5 + 2$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Add $- 5$ and $2$ .

$- z = - 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

$- z = - 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Divide each term in $- z = - 3$ by $- 1$ and simplify.

Divide each term in $- z = - 3$ by $- 1$ .

$\frac{- z}{- 1} = \frac{- 3}{- 1}$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{- 3}{- 1}$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Divide $z$ by $1$ .

$z = \frac{- 3}{- 1}$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

$z = \frac{- 3}{- 1}$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$z = 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

$z = 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

$z = 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

$z = 3$

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

$y = - \frac{7}{5} + \frac{4 z}{5}$

Step 6

Replace all occurrences of $z$ with $3$ in each equation.

Replace all occurrences of $z$ in $x = - \frac{2 (3 - z)}{5}$ with $3$ .

$x = - \frac{2 (3 - (3))}{5}$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the right side.

Simplify $- \frac{2 (3 - (3))}{5}$ .

Simplify the numerator.

Multiply $- 1$ by $3$ .

$x = - \frac{2 (3 - 3)}{5}$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Subtract $3$ from $3$ .

$x = - \frac{2 \cdot 0}{5}$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = - \frac{2 \cdot 0}{5}$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Simplify the expression.

Multiply $2$ by $0$ .

$x = - \frac{0}{5}$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Divide $0$ by $5$ .

$x = - 0$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Multiply $- 1$ by $0$ .

$x = 0$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 0$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 0$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

$x = 0$

$z = 3$

$y = - \frac{7}{5} + \frac{4 z}{5}$

Replace all occurrences of $z$ in $y = - \frac{7}{5} + \frac{4 z}{5}$ with $3$ .

$y = - \frac{7}{5} + \frac{4 (3)}{5}$

$x = 0$

$z = 3$

Simplify the right side.

Simplify $- \frac{7}{5} + \frac{4 (3)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 7 + 4 (3)}{5}$

$x = 0$

$z = 3$

Simplify the expression.

Multiply $4$ by $3$ .

$y = \frac{- 7 + 12}{5}$

$x = 0$

$z = 3$

Add $- 7$ and $12$ .

$y = \frac{5}{5}$

$x = 0$

$z = 3$

Divide $5$ by $5$ .

$y = 1$

$x = 0$

$z = 3$

$y = 1$

$x = 0$

$z = 3$

$y = 1$

$x = 0$

$z = 3$

$y = 1$

$x = 0$

$z = 3$

$y = 1$

$x = 0$

$z = 3$

Step 7

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

$(0, 1, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(0, 1, 3)$

Equation Form:

$x = 0, y = 1, z = 3$

Solve by Substitution 4x-2y-z=-5 , x-3y+2z=3 , 3x+y-2z=-5

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