Solve the system of equations by elimination. -x - 3y - 2z = -20 -2x - y + 3z = -16 x - 2y - 2z = -13 ____

Combine Equations to Eliminate x: First, let's add the first and third equations to eliminate x. (-x - 3y - 2z) + (x - 2y - 2z) = -20 + (-13) -x + x - 3y - 2y - 2z - 2z = -33 -5y - 4z = -33Multiply and Combine Equations: Now, let's multiply the second equation by 2 so we can eliminate x with the first equation. 2(-2x - y + 3z) = 2(-16) -4x - 2y + 6z = -32Solve System of Equations: Add the modified second equation to the first equation. (-x - 3y - 2z) + (-4x - 2y + 6z) = -20 + (-32) -x - 4x - 3y - 2y - 2z + 6z = -52 -5x - 5y + 4z = -52Eliminate z: Now, let's solve the system of two equations we have: -5y - 4z = -33 -5x - 5y + 4z = -52 We can add these two equations to eliminate z. (-5y - 4z) + (-5x - 5y + 4z) = -33 + (-52) -5y - 5x - 5y = -85 -5x - 10y = -85Solve for y: Divide the last equation by -5 to simplify. -5x - 10y = -85 x + 2y = 17Correct Previous Step: Now, let's solve for y using the equation -5y - 4z = -33. We can substitute x from x + 2y = 17 into this equation. But wait, I made a mistake in the previous step, I should have divided by -5 correctly. Let's correct that. -5x - 10y = -85 x + 2y = 17 should be x + 2y = -17

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Solve the system of equations by elimination. $\newline$ $-x - 3y - 2z = -20$ $\newline$ $-2x - y + 3z = -16$ $\newline$ $x - 2y - 2z = -13$

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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

-x - 3y - 2z = -20

\newline

-2x - y + 3z = -16

\newline

x - 2y - 2z = -13

Combine Equations to Eliminate x: First, let's add the first and third equations to eliminate x. $\newline$ $(-x - 3y - 2z) + (x - 2y - 2z) = -20 + (-13)$ $\newline$ $-x + x - 3y - 2y - 2z - 2z = -33$ $\newline$ $-5y - 4z = -33$
Multiply and Combine Equations: Now, let's multiply the second equation by $2$ so we can eliminate $x$ with the first equation. $\newline$ $2(-2x - y + 3z) = 2(-16)$ $\newline$ $-4x - 2y + 6z = -32$
Solve System of Equations: Add the modified second equation to the first equation. $\newline$ $(-x - 3y - 2z) + (-4x - 2y + 6z) = -20 + (-32)$ $\newline$ $-x - 4x - 3y - 2y - 2z + 6z = -52$ $\newline$ $-5x - 5y + 4z = -52$
Eliminate z: Now, let's solve the system of two equations we have: $\newline$ $-5y - 4z = -33$ $\newline$ $-5x - 5y + 4z = -52$ $\newline$ We can add these two equations to eliminate z. $\newline$ $(-5y - 4z) + (-5x - 5y + 4z) = -33 + (-52)$ $\newline$ $-5y - 5x - 5y = -85$ $\newline$ $-5x - 10y = -85$
Solve for y: Divide the last equation by $-5$ to simplify. $-5x - 10y = -85$ $x + 2y = 17$
Correct Previous Step: Now, let's solve for $y$ using the equation $-5y - 4z = -33$ . We can substitute $x$ from $x + 2y = 17$ into this equation. But wait, I made a mistake in the previous step, I should have divided by $-5$ correctly. Let's correct that. $-5x - 10y = -85$ $x + 2y = 17$ should be $x + 2y = -17$