Solve the system of equations by elimination. 2x - y + z = -6 3x - 2y + 2z = -4 -x + 3y - 2z = -20 ____

Add equations to eliminate z: First, let's add the first and third equations to eliminate z. (2x - y + z) + (-x + 3y - 2z) = -6 + (-20) 2x - y + z - x + 3y - 2z = -26 x + 2y - z = -26Multiply and add equations: Now, let's multiply the first equation by 2 and add it to the second equation to eliminate z. (2*(2x - y + z)) + (3x - 2y + 2z) = 2*(-6) + (-4) 4x - 2y + 2z + 3x - 2y + 2z = -12 - 4 7x - 4y + 4z = -16 But wait, I made a mistake here, I should have eliminated z, not kept it.

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Solve the system of equations by elimination. $\newline$ $2x - y + z = -6$ $\newline$ $3x - 2y + 2z = -4$ $\newline$ $-x + 3y - 2z = -20$

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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

2x - y + z = -6

\newline

3x - 2y + 2z = -4

\newline

-x + 3y - 2z = -20

Add equations to eliminate z: First, let's add the first and third equations to eliminate z. $\newline$ $(2x - y + z) + (-x + 3y - 2z) = -6 + (-20)$ $\newline$ $2x - y + z - x + 3y - 2z = -26$ $\newline$ $x + 2y - z = -26$
Multiply and add equations: Now, let's multiply the first equation by $2$ and add it to the second equation to eliminate $z$ .
$(2*(2x - y + z)) + (3x - 2y + 2z) = 2*(-6) + (-4)$
$4x - 2y + 2z + 3x - 2y + 2z = -12 - 4$
$7x - 4y + 4z = -16$
But wait, I made a mistake here, I should have eliminated $z$ , not kept it.