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Solve using elimination. $\newline$ $-3x + y = -17$ $\newline$ $-3x + 7y = 7$ $\newline$ (_, _)

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Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x + y = -17

\newline

-3x + 7y = 7

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-3x + y = -17$ $\newline$ $-3x + 7y = 7$
Eliminate $x$ : Since the coefficients of $x$ in both equations are the same, we can eliminate the $x$ variable by subtracting the second equation from the first. $\newline$ Subtract the second equation from the first: $\newline$ $(–3x + y) - (–3x + 7y) = –17 - 7$
Subtract Equations: Perform the subtraction to eliminate the $x$ variable. $\newline$ $-3x + y + 3x - 7y = -17 - 7$ $\newline$ $y - 7y = -17 - 7$ $\newline$ $-6y = -24$
Solve for y: Solve for y by dividing both sides of the equation by -6＂).\(\newline\$-6y / -6 = -24 / -6\)\(\newline\)\(y = 4\)
Substitute \(y\): Substitute the value of \(y\) back into one of the original equations to solve for \(x\). We can use the first equation for this purpose.\(\newline\)\(–3x + y = –17\)\(\newline\)\(–3x + 4 = –17\)
Solve for x: Solve for x by adding \(-4\) to both sides of the equation and then dividing by \(-3\).\(\newline\)\(-3x = -17 - 4\)\(\newline\)\(-3x = -21\)\(\newline\)\(x = -21 / -3\)\(\newline\)\(x = 7\)

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