Solve using elimination. –2x − 2y = 6 x + 2y = 2 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –2x − 2y = 6 x + 2y = 2Add Equations: Add the two equations together to eliminate the y variable. (–2x − 2y) + (x + 2y) = 6 + 2Find x: Perform the addition to find the value of x. –2x + x = 6 + 2 –x = 8Solve for x: Solve for x by dividing both sides by –1. x = 8 / (–1) x = –8Substitute x for y: Substitute the value of x back into one of the original equations to solve for y. We'll use the second equation: x + 2y = 2. (–8) + 2y = 2Isolate y term: Add 8 to both sides to isolate the term with y. 2y = 2 + 8 2y = 10Solve for y: Divide both sides by 2 to solve for y. y = 10 / 2 y = 5

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Solve using elimination. $\newline$ $-2x - 2y = 6$ $\newline$ $x + 2y = 2$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-2x - 2y = 6

\newline

x + 2y = 2

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-2x - 2y = 6$ $\newline$ $x + 2y = 2$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-2x - 2y) + (x + 2y) = 6 + 2$
Find $x$ : Perform the addition to find the value of $x$ .
$–2x + x = 6 + 2$
$–x = 8$
Solve for x: Solve for x by dividing both sides by $–1$ . $x = \frac{8}{(–1)}$ $x = –8$
Substitute $x$ for $y$ : Substitute the value of $x$ back into one of the original equations to solve for $y$ . We'll use the second equation: $x + 2y = 2$ . $\newline$ $(–8) + 2y = 2$
Isolate y term: Add $8$ to both sides to isolate the term with $y$ . $\newline$ $2y = 2 + 8$ $\newline$ $2y = 10$
Solve for y: Divide both sides by $2$ to solve for y. $\newline$ $y = \frac{10}{2}$ $\newline$ $y = 5$