Solve the system of equations by elimination. -3x + y - 2z = 3 2x - y + 3z = -18 x + y + 2z = -9 ____

Combine Equations to Eliminate y: Combine the first and second equations to eliminate y. (-3x + y - 2z) + (2x - y + 3z) = 3 + (-18) -3x + y - 2z + 2x - y + 3z = -15 -x + z = -15Combine Equations to Eliminate y: Combine the second and third equations to eliminate y. (2x - y + 3z) + (x + y + 2z) = -18 + (-9) 2x - y + 3z + x + y + 2z = -27 3x + 5z = -27Multiply to Eliminate x: Multiply the equation -x + z = -15 by 3 to help eliminate x when added to 3x + 5z = -27. 3(-x + z) = 3(-15) -3x + 3z = -45Add Equations to Eliminate x: Add the equations -3x + 3z = -45 and 3x + 5z = -27 to eliminate x. (-3x + 3z) + (3x + 5z) = -45 + (-27) -3x + 3z + 3x + 5z = -72 8z = -72Find z: Divide both sides by 8 to find z. 8z / 8 = -72 / 8 z = -9Find x: Substitute z = -9 into -x + z = -15 to find x. -x + (-9) = -15 -x - 9 = -15Solve for x: Add 9 to both sides to solve for x. -x - 9 + 9 = -15 + 9 -x = -6 x = 6Find y: Substitute x = 6 and z = -9 into the third equation x + y + 2z = -9 to find y. 6 + y + 2(-9) = -9 6 + y - 18 = -9Solve for y: Add 18 to both sides and then subtract 6 to solve for y. y - 18 + 18 = -9 + 18 - 6 y = 3

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Solve the system of equations by elimination. $\newline$ $-3x + y - 2z = 3$ $\newline$ $2x - y + 3z = -18$ $\newline$ $x + y + 2z = -9$

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Algebra 2

Solve a system of equations in three variables using elimination

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Q. Solve the system of equations by elimination.

\newline

-3x + y - 2z = 3

\newline

2x - y + 3z = -18

\newline

x + y + 2z = -9

Combine Equations to Eliminate $y$ : Combine the first and second equations to eliminate $y$ .
$(-3x + y - 2z) + (2x - y + 3z) = 3 + (-18)$
$-3x + y - 2z + 2x - y + 3z = -15$
$-x + z = -15$
Combine Equations to Eliminate $y$ : Combine the second and third equations to eliminate $y$ .
$(2x - y + 3z) + (x + y + 2z) = -18 + (-9)$
$2x - y + 3z + x + y + 2z = -27$
$3x + 5z = -27$
Multiply to Eliminate $x$ : Multiply the equation $-x + z = -15$ by $3$ to help eliminate $x$ when added to $3x + 5z = -27$ . $\newline$ $3(-x + z) = 3(-15)$ $\newline$ $-3x + 3z = -45$
Add Equations to Eliminate $x$ : Add the equations $-3x + 3z = -45$ and $3x + 5z = -27$ to eliminate $x$ .
$(-3x + 3z) + (3x + 5z) = -45 + (-27)$
$-3x + 3z + 3x + 5z = -72$
$8z = -72$
Find $z$ : Divide both sides by $8$ to find $z$ . $\frac{8z}{8} = \frac{-72}{8}$ $z = -9$
Find $x$ : Substitute $z = -9$ into $-x + z = -15$ to find $x$ . $\newline$ $-x + (-9) = -15$ $\newline$ $-x - 9 = -15$
Solve for x: Add $9$ to both sides to solve for x. $\newline$ $-x - 9 + 9 = -15 + 9$ $\newline$ $-x = -6$ $\newline$ $x = 6$
Find $y$ : Substitute $x = 6$ and $z = -9$ into the third equation $x + y + 2z = -9$ to find $y$ . $6 + y + 2(-9) = -9$ $6 + y - 18 = -9$
Solve for y: Add $18$ to both sides and then subtract $6$ to solve for $y$ . $\newline$ $y - 18 + 18 = -9 + 18 - 6$ $\newline$ $y = 3$