Solve using elimination. –5x + 3y = 16 5x − 7y = 16 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –5x + 3y = 16 5x − 7y = 16Add Equations: Add the two equations together to eliminate the x variable. (–5x + 3y) + (5x − 7y) = 16 + 16Eliminate x: Perform the addition to eliminate the x variable and simplify the equation. –5x + 5x + 3y − 7y = 32 0x − 4y = 32Solve for y: Simplify the equation further to solve for y. −4y = 32 y = 32 / (−4) y = −8Substitute and Solve: Substitute y = −8 back into one of the original equations to solve for x. We can use the first equation: –5x + 3y = 16. –5x + 3(−8) = 16 –5x − 24 = 16Isolate x: Add 24 to both sides of the equation to isolate the term with x. –5x − 24 + 24 = 16 + 24 –5x = 40Final Solution: Divide both sides by -5 to solve for x. x = 40 / (−5) x = −8

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Solve using elimination. $\newline$ $-5x + 3y = 16$ $\newline$ $5x - 7y = 16$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-5x + 3y = 16

\newline

5x - 7y = 16

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-5x + 3y = 16$ $\newline$ $5x - 7y = 16$
Add Equations: Add the two equations together to eliminate the $x$ variable. $\newline$ $(-5x + 3y) + (5x − 7y) = 16 + 16$
Eliminate x: Perform the addition to eliminate the x variable and simplify the equation. $\newline$ $-5x + 5x + 3y - 7y = 32$ $\newline$ $0x - 4y = 32$
Solve for y: Simplify the equation further to solve for y. $\newline$ $-4y = 32$ $\newline$ $y = \frac{32}{(-4)}$ $\newline$ $y = -8$
Substitute and Solve: Substitute $y = -8$ back into one of the original equations to solve for $x$ . We can use the first equation: $-5x + 3y = 16$ .
$-5x + 3(-8) = 16$
$-5x - 24 = 16$
Isolate x: Add $24$ to both sides of the equation to isolate the term with $x$ . $\newline$ $-5x - 24 + 24 = 16 + 24$ $\newline$ $-5x = 40$
Final Solution: Divide both sides by $-5$ to solve for $x$ . $x = \frac{40}{(−5)}$ $x = −8$