Solve the System of Equations x-2y+2z=9 y+2z=5 z=3

$x - 2 y + 2 z = 9$ $y + 2 z = 5$ $z = 3$

Step 1

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

Replace all occurrences of $z$ in $x - 2 y + 2 z = 9$ with $3$ .

$x - 2 y + 2 (3) = 9$

$z = 3$

$y + 2 z = 5$

Simplify the left side.

Multiply $2$ by $3$ .

$x - 2 y + 6 = 9$

$z = 3$

$y + 2 z = 5$

$x - 2 y + 6 = 9$

$z = 3$

$y + 2 z = 5$

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

$y + 2 (3) = 5$

$x - 2 y + 6 = 9$

$z = 3$

Simplify the left side.

Multiply $2$ by $3$ .

$y + 6 = 5$

$x - 2 y + 6 = 9$

$z = 3$

$y + 6 = 5$

$x - 2 y + 6 = 9$

$z = 3$

$y + 6 = 5$

$x - 2 y + 6 = 9$

$z = 3$

Step 2

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

Subtract $6$ from both sides of the equation.

$y = 5 - 6$

$x - 2 y + 6 = 9$

$z = 3$

Subtract $6$ from $5$ .

$y = - 1$

$x - 2 y + 6 = 9$

$z = 3$

$y = - 1$

$x - 2 y + 6 = 9$

$z = 3$

Step 3

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

Replace all occurrences of $y$ in $x - 2 y + 6 = 9$ with $- 1$ .

$x - 2 \cdot - 1 + 6 = 9$

$y = - 1$

$z = 3$

Simplify the left side.

Simplify $x - 2 \cdot - 1 + 6$ .

Multiply $- 2$ by $- 1$ .

$x + 2 + 6 = 9$

$y = - 1$

$z = 3$

Add $2$ and $6$ .

$x + 8 = 9$

$y = - 1$

$z = 3$

$x + 8 = 9$

$y = - 1$

$z = 3$

$x + 8 = 9$

$y = - 1$

$z = 3$

$x + 8 = 9$

$y = - 1$

$z = 3$

Step 4

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

Subtract $8$ from both sides of the equation.

$x = 9 - 8$

$y = - 1$

$z = 3$

Subtract $8$ from $9$ .

$x = 1$

$y = - 1$

$z = 3$

$x = 1$

$y = - 1$

$z = 3$

Step 5

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

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

Step 6

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

$(1, - 1, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, - 1, 3)$

Equation Form:

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

Solve the System of Equations x-2y+2z=9 y+2z=5 z=3

Related Questions

Support LCMGCF.com by disabling your adblocker.