Solve the System of Equations 2x+z=-5 3x+y=-10 3y-4z=-6

$2 x + z = - 5$ $3 x + y = - 10$ $3 y - 4 z = - 6$

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

$z = - 5 - 2 x$

$3 x + y = - 10$

$3 y - 4 z = - 6$

Replace all occurrences of $z$ with $- 5 - 2 x$ in each equation.

Replace all occurrences of $z$ in $3 y - 4 z = - 6$ with $- 5 - 2 x$ .

$3 y - 4 (- 5 - 2 x) = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$3 y - 4 \cdot - 5 - 4 (- 2 x) = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

Multiply $- 4$ by $- 5$ .

$3 y + 20 - 4 (- 2 x) = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

Multiply $- 2$ by $- 4$ .

$3 y + 20 + 8 x = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

$3 y + 20 + 8 x = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

$3 y + 20 + 8 x = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

$3 y + 20 + 8 x = - 6$

$z = - 5 - 2 x$

$3 x + y = - 10$

Reorder $- 5$ and $- 2 x$ .

$z = - 2 x - 5$

$3 y + 20 + 8 x = - 6$

$3 x + y = - 10$

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

$y = - 10 - 3 x$

$z = - 2 x - 5$

$3 y + 20 + 8 x = - 6$

Replace all occurrences of $y$ with $- 10 - 3 x$ in each equation.

Replace all occurrences of $y$ in $3 y + 20 + 8 x = - 6$ with $- 10 - 3 x$ .

$3 (- 10 - 3 x) + 20 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Simplify the left side.

Simplify $3 (- 10 - 3 x) + 20 + 8 x$ .

Simplify each term.

Apply the distributive property.

$3 \cdot - 10 + 3 (- 3 x) + 20 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Multiply $3$ by $- 10$ .

$- 30 + 3 (- 3 x) + 20 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Multiply $- 3$ by $3$ .

$- 30 - 9 x + 20 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- 30 - 9 x + 20 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Simplify by adding terms.

Add $- 30$ and $20$ .

$- 9 x - 10 + 8 x = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Add $- 9 x$ and $8 x$ .

$- x - 10 = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- x - 10 = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- x - 10 = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- x - 10 = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- x - 10 = - 6$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Solve for $x$ in $- x - 10 = - 6$ .

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

Add $10$ to both sides of the equation.

$- x = - 6 + 10$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Add $- 6$ and $10$ .

$- x = 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$- x = 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Divide each term in $- x = 4$ by $- 1$ and simplify.

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$x = \frac{4}{- 1}$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Simplify the right side.

Divide $4$ by $- 1$ .

$x = - 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$x = - 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$x = - 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

$x = - 4$

$y = - 10 - 3 x$

$z = - 2 x - 5$

Replace all occurrences of $x$ with $- 4$ in each equation.

Replace all occurrences of $x$ in $y = - 10 - 3 x$ with $- 4$ .

$y = - 10 - 3 \cdot - 4$

$x = - 4$

$z = - 2 x - 5$

Simplify the right side.

Simplify $- 10 - 3 \cdot - 4$ .

Multiply $- 3$ by $- 4$ .

$y = - 10 + 12$

$x = - 4$

$z = - 2 x - 5$

Add $- 10$ and $12$ .

$y = 2$

$x = - 4$

$z = - 2 x - 5$

$y = 2$

$x = - 4$

$z = - 2 x - 5$

$y = 2$

$x = - 4$

$z = - 2 x - 5$

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

$z = - 2 \cdot - 4 - 5$

$y = 2$

$x = - 4$

Simplify the right side.

Simplify $- 2 \cdot - 4 - 5$ .

Multiply $- 2$ by $- 4$ .

$z = 8 - 5$

$y = 2$

$x = - 4$

Subtract $5$ from $8$ .

$z = 3$

$y = 2$

$x = - 4$

$z = 3$

$y = 2$

$x = - 4$

$z = 3$

$y = 2$

$x = - 4$

$z = 3$

$y = 2$

$x = - 4$

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

$(- 4, 2, 3)$

The result can be shown in multiple forms.

Point Form:

$(- 4, 2, 3)$

Equation Form:

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

Solve the System of Equations 2x+z=-5 3x+y=-10 3y-4z=-6

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