Solve using elimination. 10x − 7y = 18 –8x + 7y = –6 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 10x − 7y = 18 –8x + 7y = –6Add Equations: Add the two equations together to eliminate the y variable. (10x − 7y) + (−8x + 7y) = 18 + (−6) 10x − 7y − 8x + 7y = 18 − 6 2x = 12Solve for x: Solve for x by dividing both sides of the equation by 2. 2x = 12 x = 12 / 2 x = 6Substitute x: Substitute the value of x back into one of the original equations to solve for y. We'll use the first equation. 10x − 7y = 18 10(6) − 7y = 18 60 − 7y = 18Isolate y: Isolate the y variable by subtracting 60 from both sides of the equation. 60 − 7y − 60 = 18 − 60 −7y = −42Solve for y: Solve for y by dividing both sides of the equation by -7. −7y = −42 y = −42 / (−7) y = 6

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Solve using elimination. $\newline$ $10x - 7y = 18$ $\newline$ $-8x + 7y = -6$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

10x - 7y = 18

\newline

-8x + 7y = -6

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $10x − 7y = 18$ $\newline$ $−8x + 7y = −6$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(10x − 7y) + (−8x + 7y) = 18 + (−6)$ $\newline$ $10x − 7y − 8x + 7y = 18 − 6$ $\newline$ $2x = 12$
Solve for x: Solve for x by dividing both sides of the equation by $2$ . $\newline$ $2x = 12$ $\newline$ $x = \frac{12}{2}$ $\newline$ $x = 6$
Substitute x: Substitute the value of $x$ back into one of the original equations to solve for $y$ . We'll use the first equation. $\newline$ $10x - 7y = 18$ $\newline$ $10(6) - 7y = 18$ $\newline$ $60 - 7y = 18$
Isolate y: Isolate the $y$ variable by subtracting $60$ from both sides of the equation. $60 − 7y − 60 = 18 − 60$ $−7y = −42$
Solve for y: Solve for y by dividing both sides of the equation by $-7$ . $\newline$ $-7y = -42$ $\newline$ $y = -42 / (-7)$ $\newline$ $y = 6$