Solve the System of Equations x+2y-5z=10 y+2z=2 z=-1

$x + 2 y - 5 z = 10$ $y + 2 z = 2$ $z = - 1$

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

Replace all occurrences of $z$ in $x + 2 y - 5 z = 10$ with $- 1$ .

$x + 2 y - 5 \cdot - 1 = 10$

$z = - 1$

$y + 2 z = 2$

Simplify the left side.

Multiply $- 5$ by $- 1$ .

$x + 2 y + 5 = 10$

$z = - 1$

$y + 2 z = 2$

$x + 2 y + 5 = 10$

$z = - 1$

$y + 2 z = 2$

Replace all occurrences of $z$ in $y + 2 z = 2$ with $- 1$ .

$y + 2 (- 1) = 2$

$x + 2 y + 5 = 10$

$z = - 1$

Simplify the left side.

Multiply $2$ by $- 1$ .

$y - 2 = 2$

$x + 2 y + 5 = 10$

$z = - 1$

$y - 2 = 2$

$x + 2 y + 5 = 10$

$z = - 1$

$y - 2 = 2$

$x + 2 y + 5 = 10$

$z = - 1$

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

Add $2$ to both sides of the equation.

$y = 2 + 2$

$x + 2 y + 5 = 10$

$z = - 1$

Add $2$ and $2$ .

$y = 4$

$x + 2 y + 5 = 10$

$z = - 1$

$y = 4$

$x + 2 y + 5 = 10$

$z = - 1$

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x + 2 y + 5 = 10$ with $4$ .

$x + 2 (4) + 5 = 10$

$y = 4$

$z = - 1$

Simplify the left side.

Simplify $x + 2 (4) + 5$ .

Multiply $2$ by $4$ .

$x + 8 + 5 = 10$

$y = 4$

$z = - 1$

Add $8$ and $5$ .

$x + 13 = 10$

$y = 4$

$z = - 1$

$x + 13 = 10$

$y = 4$

$z = - 1$

$x + 13 = 10$

$y = 4$

$z = - 1$

$x + 13 = 10$

$y = 4$

$z = - 1$

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

Subtract $13$ from both sides of the equation.

$x = 10 - 13$

$y = 4$

$z = - 1$

Subtract $13$ from $10$ .

$x = - 3$

$y = 4$

$z = - 1$

$x = - 3$

$y = 4$

$z = - 1$

Solve the system of equations $x = - 3 y = 4 z = - 1$ .

$x = - 3 y = 4 z = - 1$

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

$(- 3, 4, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 3, 4, - 1)$

Equation Form:

$x = - 3, y = 4, z = - 1$

Solve the System of Equations x+2y-5z=10 y+2z=2 z=-1

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