Solve using elimination. 2x + 3y = –20 –2x − y = 8 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 2x + 3y = –20 –2x − y = 8Add Equations: Add the two equations together to eliminate the variable x. (2x + 3y) + (–2x − y) = –20 + 8Eliminate x: Perform the addition to eliminate x and simplify the equation for y. 2x - 2x + 3y - y = -20 + 8 0x + 2y = -12Solve for y: Simplify the equation further to solve for y. 2y = -12 y = -12 / 2 y = -6Substitute for x: 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. 2x + 3(-6) = –20 2x - 18 = -20Isolate x: Add 18 to both sides of the equation to isolate the term with x. 2x - 18 + 18 = -20 + 18 2x = -2Final Solution: Divide both sides of the equation by 2 to solve for x. 2x / 2 = -2 / 2 x = -1

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Solve using elimination. $\newline$ $2x + 3y = -20$ $\newline$ $-2x - y = 8$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

2x + 3y = -20

\newline

-2x - y = 8

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $2x + 3y = -20$ $\newline$ $-2x - y = 8$
Add Equations: Add the two equations together to eliminate the variable $x$ . $\newline$ $(2x + 3y) + (–2x − y) = –20 + 8$
Eliminate $x$ : Perform the addition to eliminate $x$ and simplify the equation for $y$ . $2x - 2x + 3y - y = -20 + 8$ $0x + 2y = -12$
Solve for y: Simplify the equation further to solve for y. $\newline$ $2y = -12$ $\newline$ $y = \frac{-12}{2}$ $\newline$ $y = -6$
Substitute for x: 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. $\newline$ $2x + 3(-6) = -20$ $\newline$ $2x - 18 = -20$
Isolate x: Add $18$ to both sides of the equation to isolate the term with $x$ . $\newline$ $2x - 18 + 18 = -20 + 18$ $\newline$ $2x = -2$
Final Solution: Divide both sides of the equation by $2$ to solve for $x$ . $\frac{2x}{2} = \frac{-2}{2}$ $x = -1$