Solve using elimination. 9x − 7y = –16 –10x + 7y = 10 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 9x − 7y = –16 –10x + 7y = 10Add Equations: Add the two equations together to eliminate the y variable. (9x − 7y) + (−10x + 7y) = (−16) + (10)Find x: Perform the addition to find the value of x. 9x − 10x = −16 + 10 −1x = −6 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. 9(6) − 7y = –16 54 − 7y = –16Isolate y: Isolate the y variable by subtracting 54 from both sides of the equation. −7y = –16 − 54 −7y = –70 y = 10Check Solution: Check the solution by substituting both x and y values into the second original equation. −10(6) + 7(10) = 10 −60 + 70 = 10 10 = 10 The solution checks out.

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Solve using elimination. $\newline$ $9x - 7y = -16$ $\newline$ $-10x + 7y = 10$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

9x - 7y = -16

\newline

-10x + 7y = 10

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $9x − 7y = −16$ $\newline$ $−10x + 7y = 10$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(9x − 7y) + (−10x + 7y) = (−16) + (10)$
Find $x$ : Perform the addition to find the value of $x$ . $9x − 10x = −16 + 10$ $−1x = −6$ $x = 6$
Substitute $x$ : Substitute the value of $x$ back into one of the original equations to solve for $y$ . We'll use the first equation. $9(6) − 7y = −16$ $54 − 7y = −16$
Isolate y: Isolate the $y$ variable by subtracting $54$ from both sides of the equation. $\newline$ $−7y = −16 − 54$ $\newline$ $−7y = −70$ $\newline$ $y = 10$
Check Solution: Check the solution by substituting both $x$ and $y$ values into the second original equation.$\newline$ $-10(6) + 7(10) = 10$ $\newline$ $-60 + 70 = 10$ $\newline$ $10 = 10$ $\newline$The solution checks out.