Solve the System of Equations 2x-3y-5z=-19 3x-4y+z=-2 x+y+z=6

$2 x - 3 y - 5 z = - 19$ $3 x - 4 y + z = - 2$ $x + y + z = 6$

Step 1

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

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

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

$2 x - 3 y - 5 z = - 19$

$x + y + z = 6$

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

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

$2 x - 3 y - 5 z = - 19$

$x + y + z = 6$

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

$2 x - 3 y - 5 z = - 19$

$x + y + z = 6$

Step 2

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

Replace all occurrences of $z$ in $2 x - 3 y - 5 z = - 19$ with $- 2 - 3 x + 4 y$ .

$2 x - 3 y - 5 (- 2 - 3 x + 4 y) = - 19$

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

$x + y + z = 6$

Simplify the left side.

Simplify $2 x - 3 y - 5 (- 2 - 3 x + 4 y)$ .

Simplify each term.

Apply the distributive property.

$2 x - 3 y - 5 \cdot - 2 - 5 (- 3 x) - 5 (4 y) = - 19$

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

$x + y + z = 6$

Simplify.

Multiply $- 5$ by $- 2$ .

$2 x - 3 y + 10 - 5 (- 3 x) - 5 (4 y) = - 19$

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

$x + y + z = 6$

Multiply $- 3$ by $- 5$ .

$2 x - 3 y + 10 + 15 x - 5 (4 y) = - 19$

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

$x + y + z = 6$

Multiply $4$ by $- 5$ .

$2 x - 3 y + 10 + 15 x - 20 y = - 19$

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

$x + y + z = 6$

$2 x - 3 y + 10 + 15 x - 20 y = - 19$

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

$x + y + z = 6$

$2 x - 3 y + 10 + 15 x - 20 y = - 19$

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

$x + y + z = 6$

Simplify by adding terms.

Add $2 x$ and $15 x$ .

$17 x - 3 y + 10 - 20 y = - 19$

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

$x + y + z = 6$

Subtract $20 y$ from $- 3 y$ .

$17 x - 23 y + 10 = - 19$

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

$x + y + z = 6$

$17 x - 23 y + 10 = - 19$

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

$x + y + z = 6$

$17 x - 23 y + 10 = - 19$

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

$x + y + z = 6$

$17 x - 23 y + 10 = - 19$

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

$x + y + z = 6$

Replace all occurrences of $z$ in $x + y + z = 6$ with $- 2 - 3 x + 4 y$ .

$x + y - 2 - 3 x + 4 y = 6$

$17 x - 23 y + 10 = - 19$

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

Simplify the left side.

Simplify $x + y - 2 - 3 x + 4 y$ .

Remove parentheses.

$x + y - 2 - 3 x + 4 y = 6$

$17 x - 23 y + 10 = - 19$

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

Subtract $3 x$ from $x$ .

$- 2 x + y - 2 + 4 y = 6$

$17 x - 23 y + 10 = - 19$

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

Add $y$ and $4 y$ .

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

$17 x - 23 y + 10 = - 19$

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

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

$17 x - 23 y + 10 = - 19$

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

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

$17 x - 23 y + 10 = - 19$

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

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

$17 x - 23 y + 10 = - 19$

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

Step 3

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

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

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

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

$17 x - 23 y + 10 = - 19$

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

Add $2$ to both sides of the equation.

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

$17 x - 23 y + 10 = - 19$

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

Add $6$ and $2$ .

$- 2 x = - 5 y + 8$

$17 x - 23 y + 10 = - 19$

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

$- 2 x = - 5 y + 8$

$17 x - 23 y + 10 = - 19$

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

Divide each term in $- 2 x = - 5 y + 8$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 5 y + 8$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 5 y}{- 2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 5 y}{- 2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

Divide $x$ by $1$ .

$x = \frac{- 5 y}{- 2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{- 5 y}{- 2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{- 5 y}{- 2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{(5) y}{2} + \frac{8}{- 2}$

$17 x - 23 y + 10 = - 19$

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

Divide $8$ by $- 2$ .

$x = \frac{5 y}{2} - 4$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{5 y}{2} - 4$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{5 y}{2} - 4$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{5 y}{2} - 4$

$17 x - 23 y + 10 = - 19$

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

$x = \frac{5 y}{2} - 4$

$17 x - 23 y + 10 = - 19$

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

Step 4

Replace all occurrences of $x$ with $\frac{5 y}{2} - 4$ in each equation.

Replace all occurrences of $x$ in $17 x - 23 y + 10 = - 19$ with $\frac{5 y}{2} - 4$ .

$17 (\frac{5 y}{2} - 4) - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Simplify the left side.

Simplify $17 (\frac{5 y}{2} - 4) - 23 y + 10$ .

Simplify each term.

Apply the distributive property.

$17 (\frac{5 y}{2}) + 17 \cdot - 4 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $17 \frac{5 y}{2}$ .

Combine $17$ and $\frac{5 y}{2}$ .

$\frac{17 (5 y)}{2} + 17 \cdot - 4 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $5$ by $17$ .

$\frac{85 y}{2} + 17 \cdot - 4 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{85 y}{2} + 17 \cdot - 4 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $17$ by $- 4$ .

$\frac{85 y}{2} - 68 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{85 y}{2} - 68 - 23 y + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

To write $- 23 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{85 y}{2} - 23 y \cdot \frac{2}{2} - 68 + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Combine $- 23 y$ and $\frac{2}{2}$ .

$\frac{85 y}{2} + \frac{- 23 y \cdot 2}{2} - 68 + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Combine the numerators over the common denominator.

$\frac{85 y - 23 y \cdot 2}{2} - 68 + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Find the common denominator.

Write $- 68$ as a fraction with denominator $1$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68}{1} + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $\frac{- 68}{1}$ by $\frac{2}{2}$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68}{1} \cdot \frac{2}{2} + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $\frac{- 68}{1}$ by $\frac{2}{2}$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68 \cdot 2}{2} + 10 = - 19$

$x = \frac{5 y}{2} - 4$

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

Write $10$ as a fraction with denominator $1$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68 \cdot 2}{2} + \frac{10}{1} = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $\frac{10}{1}$ by $\frac{2}{2}$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68 \cdot 2}{2} + \frac{10}{1} \cdot \frac{2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $\frac{10}{1}$ by $\frac{2}{2}$ .

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68 \cdot 2}{2} + \frac{10 \cdot 2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{85 y - 23 y \cdot 2}{2} + \frac{- 68 \cdot 2}{2} + \frac{10 \cdot 2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Combine the numerators over the common denominator.

$\frac{85 y - 23 y \cdot 2 - 68 \cdot 2 + 10 \cdot 2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Simplify each term.

Multiply $2$ by $- 23$ .

$\frac{85 y - 46 y - 68 \cdot 2 + 10 \cdot 2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $- 68$ by $2$ .

$\frac{85 y - 46 y - 136 + 10 \cdot 2}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Multiply $10$ by $2$ .

$\frac{85 y - 46 y - 136 + 20}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{85 y - 46 y - 136 + 20}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Simplify by adding terms.

Subtract $46 y$ from $85 y$ .

$\frac{39 y - 136 + 20}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

Add $- 136$ and $20$ .

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

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

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Simplify the right side.

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

Simplify each term.

Apply the distributive property.

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Multiply $- 3 \frac{5 y}{2}$ .

Combine $- 3$ and $\frac{5 y}{2}$ .

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Multiply $5$ by $- 3$ .

$z = - 2 + \frac{- 15 y}{2} - 3 \cdot - 4 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

$z = - 2 + \frac{- 15 y}{2} - 3 \cdot - 4 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Multiply $- 3$ by $- 4$ .

$z = - 2 + \frac{- 15 y}{2} + 12 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Move the negative in front of the fraction.

$z = - 2 - \frac{15 y}{2} + 12 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

$z = - 2 - \frac{15 y}{2} + 12 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Add $- 2$ and $12$ .

$z = - \frac{15 y}{2} + 10 + 4 y$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$z = - \frac{15 y}{2} + 4 y \cdot \frac{2}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Simplify terms.

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

$z = - \frac{15 y}{2} + \frac{4 y \cdot 2}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Combine the numerators over the common denominator.

$z = \frac{- 15 y + 4 y \cdot 2}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

$z = \frac{- 15 y + 4 y \cdot 2}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $- 15 y + 4 y \cdot 2$ .

Factor $y$ out of $- 15 y$ .

$z = \frac{y \cdot - 15 + 4 y \cdot 2}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Factor $y$ out of $4 y \cdot 2$ .

$z = \frac{y \cdot - 15 + y (4 \cdot 2)}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Factor $y$ out of $y \cdot - 15 + y (4 \cdot 2)$ .

$z = \frac{y (- 15 + 4 \cdot 2)}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

$z = \frac{y (- 15 + 4 \cdot 2)}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Multiply $4$ by $2$ .

$z = \frac{y (- 15 + 8)}{2} + 10$

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Add $- 15$ and $8$ .

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Move $- 7$ to the left of $y$ .

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Move the negative in front of the fraction.

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

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

$\frac{39 y - 116}{2} = - 19$

$x = \frac{5 y}{2} - 4$

Step 5

Solve for $y$ in $\frac{39 y - 116}{2} = - 19$ .

Multiply both sides by $2$ .

$\frac{39 y - 116}{2} \cdot 2 = - 19 \cdot 2$

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

$x = \frac{5 y}{2} - 4$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{39 y - 116}{2} \cdot 2 = - 19 \cdot 2$

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

$x = \frac{5 y}{2} - 4$

Rewrite the expression.

$39 y - 116 = - 19 \cdot 2$

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

$x = \frac{5 y}{2} - 4$

$39 y - 116 = - 19 \cdot 2$

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

$x = \frac{5 y}{2} - 4$

$39 y - 116 = - 19 \cdot 2$

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

$x = \frac{5 y}{2} - 4$

Simplify the right side.

Multiply $- 19$ by $2$ .

$39 y - 116 = - 38$

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

$x = \frac{5 y}{2} - 4$

$39 y - 116 = - 38$

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

$x = \frac{5 y}{2} - 4$

$39 y - 116 = - 38$

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

$x = \frac{5 y}{2} - 4$

Solve for $y$ .

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

Add $116$ to both sides of the equation.

$39 y = - 38 + 116$

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

$x = \frac{5 y}{2} - 4$

Add $- 38$ and $116$ .

$39 y = 78$

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

$x = \frac{5 y}{2} - 4$

$39 y = 78$

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

$x = \frac{5 y}{2} - 4$

Divide each term in $39 y = 78$ by $39$ and simplify.

Divide each term in $39 y = 78$ by $39$ .

$\frac{39 y}{39} = \frac{78}{39}$

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

$x = \frac{5 y}{2} - 4$

Simplify the left side.

Cancel the common factor of $39$ .

Cancel the common factor.

$\frac{39 y}{39} = \frac{78}{39}$

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

$x = \frac{5 y}{2} - 4$

Divide $y$ by $1$ .

$y = \frac{78}{39}$

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

$x = \frac{5 y}{2} - 4$

$y = \frac{78}{39}$

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

$x = \frac{5 y}{2} - 4$

$y = \frac{78}{39}$

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

$x = \frac{5 y}{2} - 4$

Simplify the right side.

Divide $78$ by $39$ .

$y = 2$

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

$x = \frac{5 y}{2} - 4$

$y = 2$

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

$x = \frac{5 y}{2} - 4$

$y = 2$

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

$x = \frac{5 y}{2} - 4$

$y = 2$

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

$x = \frac{5 y}{2} - 4$

$y = 2$

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

$x = \frac{5 y}{2} - 4$

Step 6

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $z = - \frac{7 y}{2} + 10$ with $2$ .

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

$y = 2$

$x = \frac{5 y}{2} - 4$

Simplify the right side.

Simplify $- \frac{7 (2)}{2} + 10$ .

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$y = 2$

$x = \frac{5 y}{2} - 4$

Divide $7$ by $1$ .

$z = - 1 \cdot 7 + 10$

$y = 2$

$x = \frac{5 y}{2} - 4$

$z = - 1 \cdot 7 + 10$

$y = 2$

$x = \frac{5 y}{2} - 4$

Multiply $- 1$ by $7$ .

$z = - 7 + 10$

$y = 2$

$x = \frac{5 y}{2} - 4$

$z = - 7 + 10$

$y = 2$

$x = \frac{5 y}{2} - 4$

Add $- 7$ and $10$ .

$z = 3$

$y = 2$

$x = \frac{5 y}{2} - 4$

$z = 3$

$y = 2$

$x = \frac{5 y}{2} - 4$

$z = 3$

$y = 2$

$x = \frac{5 y}{2} - 4$

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

$x = \frac{5 (2)}{2} - 4$

$z = 3$

$y = 2$

Simplify the right side.

Simplify $\frac{5 (2)}{2} - 4$ .

Multiply $5$ by $2$ .

$x = \frac{10}{2} - 4$

$z = 3$

$y = 2$

Divide $10$ by $2$ .

$x = 5 - 4$

$z = 3$

$y = 2$

Subtract $4$ from $5$ .

$x = 1$

$z = 3$

$y = 2$

$x = 1$

$z = 3$

$y = 2$

$x = 1$

$z = 3$

$y = 2$

$x = 1$

$z = 3$

$y = 2$

Step 7

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

$(1, 2, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, 2, 3)$

Equation Form:

$x = 1, y = 2, z = 3$

Solve the System of Equations 2x-3y-5z=-19 3x-4y+z=-2 x+y+z=6

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