Solve using elimination. –3x − 6y = 12 3x + 7y = –18 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –3x − 6y = 12 3x + 7y = –18Add Equations: Add the two equations together to eliminate the x variable. (–3x − 6y) + (3x + 7y) = 12 + (–18)Perform Addition: Perform the addition to eliminate the x variable. –3x + 3x − 6y + 7y = 12 − 18 0x + 1y = –6 This simplifies to y = –6.Substitute and Solve (y): Substitute y = –6 into one of the original equations to solve for x. We'll use the first equation. –3x − 6(–6) = 12Perform Multiplication: Perform the multiplication and solve for x. –3x + 36 = 12Isolate x: Subtract 36 from both sides of the equation to isolate the term with x. –3x + 36 − 36 = 12 − 36 –3x = –24Divide and Solve (x): Divide both sides by –3 to solve for x. –3x / –3 = –24 / –3 x = 8Write Solution: Write down the solution to the system of equations. The solution is (x, y) = (8, –6).

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Solve using elimination. $\newline$ $-3x - 6y = 12$ $\newline$ $3x + 7y = -18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x - 6y = 12

\newline

3x + 7y = -18

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-3x - 6y = 12$ $\newline$ $3x + 7y = -18$
Add Equations: Add the two equations together to eliminate the $x$ variable. $\newline$ $(-3x - 6y) + (3x + 7y) = 12 + (-18)$
Perform Addition: Perform the addition to eliminate the $x$ variable. $\,-3x + 3x - 6y + 7y = 12 - 18$ $\,0x + 1y = -6$ This simplifies to $y = -6$ .
Substitute and Solve ( $y$ ): Substitute $y = -6$ into one of the original equations to solve for $x$ . We'll use the first equation. $\newline$ $-3x - 6(-6) = 12$
Perform Multiplication: Perform the multiplication and solve for $x$ . $\,-3x + 36 = 12$
Isolate x: Subtract $36$ from both sides of the equation to isolate the term with $x$ . $\newline$ $-3x + 36 - 36 = 12 - 36$ $\newline$ $-3x = -24$
Divide and Solve $x$ : Divide both sides by $–3$ to solve for $x$ . $\frac{–3x}{–3} = \frac{–24}{–3}$ $x = 8$
Write Solution: Write down the solution to the system of equations. $\newline$ The solution is $(x, y) = (8, -6)$ .