Solve using elimination. –7x − 8y = –15 8x + 8y = 8 (_____, _____)

Write Equations: Write down the system of equations. –7x − 8y = –15 8x + 8y = 8Add Equations: Add the two equations together to eliminate the y variable. (–7x − 8y) + (8x + 8y) = (–15) + (8)Perform Addition: Perform the addition. –7x + 8x = 1x –8y + 8y = 0y (which cancels out) –15 + 8 = –7 This simplifies to: x = –7Solve for x: Substitute x = –7 into one of the original equations to solve for y. We'll use the first equation. –7(–7) − 8y = –15Substitute x: Perform the multiplication. 49 − 8y = –15Perform Multiplication: Subtract 49 from both sides to isolate the term with y. 49 − 8y − 49 = –15 − 49Isolate y Term: Simplify the equation. –8y = –64Simplify Equation: Divide both sides by –8 to solve for y. –8y / –8 = –64 / –8Divide by -8: Calculate the value of y. y = 8

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Solve using elimination. $\newline$ $-7x - 8y = -15$ $\newline$ $8x + 8y = 8$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-7x - 8y = -15

\newline

8x + 8y = 8

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-7x - 8y = -15$ $\newline$ $8x + 8y = 8$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-7x - 8y) + (8x + 8y) = (-15) + (8)$
Perform Addition: Perform the addition. $\newline$ $-7x + 8x = 1x$ $\newline$ $-8y + 8y = 0y$ (which cancels out) $\newline$ $-15 + 8 = -7$ $\newline$ This simplifies to: $\newline$ $x = -7$
Solve for $x$ : Substitute $x = -7$ into one of the original equations to solve for $y$ . We'll use the first equation. $\,-7(-7) - 8y = -15$
Substitute $x$ : Perform the multiplication. $49 − 8y = −15$
Perform Multiplication: Subtract $49$ from both sides to isolate the term with $y$ . $\newline$ $49 - 8y - 49 = -15 - 49$
Isolate y Term: Simplify the equation. $-8y = -64$
Simplify Equation: Divide both sides by $–8$ to solve for $y$ . $\frac{–8y}{–8} = \frac{–64}{–8}$
Divide by $-8$ : Calculate the value of $y$ . $y = 8$