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

Eliminate y by adding equations: Add the first and second equations to eliminate y. (x - 2y - 3z) + (x + 2y + 2z) = -3 + (-2) 2x - z = -5Eliminate x by adding equations: Add the first and third equations to eliminate x. (x - 2y - 3z) + (-x + y + z) = -3 + 2 -y - 2z = -1Eliminate y by multiplying and adding equations: Multiply the second equation by 2 and add it to the third equation to eliminate y. 2(x + 2y + 2z) + (-x + y + z) = 2(-2) + 2 2x + 4y + 4z - x + y + z = -4 + 2 x + 5y + 5z = -2

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

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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 - 2y - 3z = -3

\newline

x + 2y + 2z = -2

\newline

-x + y + z = 2

Eliminate $y$ by adding equations: Add the first and second equations to eliminate $y$ . $(x - 2y - 3z) + (x + 2y + 2z) = -3 + (-2)$ $2x - z = -5$
Eliminate $x$ by adding equations: Add the first and third equations to eliminate $x$ . $(x - 2y - 3z) + (-x + y + z) = -3 + 2$ $-y - 2z = -1$
Eliminate $y$ by multiplying and adding equations: Multiply the second equation by $2$ and add it to the third equation to eliminate $y$ . $\newline$ $2(x + 2y + 2z) + (-x + y + z) = 2(-2) + 2$ $\newline$ $2x + 4y + 4z - x + y + z = -4 + 2$ $\newline$ $x + 5y + 5z = -2$