Solve using elimination. –9x − 4y = 9 10x + 4y = –14 (_____, _____)

Write Equations: Write down the system of equations. –9x − 4y = 9 10x + 4y = –14Add Equations: Add the two equations together to eliminate the y variable. (–9x − 4y) + (10x + 4y) = 9 + (–14)Find x Value: Perform the addition to find the value of x. –9x + 10x = 1x −4y + 4y = 0y (which cancels out) 9 − 14 = –5 So, 1x = –5Solve for x: Solve for x. x = –5Substitute for y: Substitute the value of x back into one of the original equations to find the value of y. We'll use the first equation. –9(–5) − 4y = 9Simplify Equation: Perform the multiplication to simplify the equation. 45 − 4y = 9Isolate y Term: Subtract 45 from both sides of the equation to isolate the term containing y. 45 − 4y − 45 = 9 − 45 −4y = –36Solve for y: Divide both sides by -4 to solve for y. −4y / -4 = –36 / -4 y = 9

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Solve using elimination. $\newline$ $-9x - 4y = 9$ $\newline$ $10x + 4y = -14$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-9x - 4y = 9

\newline

10x + 4y = -14

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-9x - 4y = 9$ $\newline$ $10x + 4y = -14$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-9x - 4y) + (10x + 4y) = 9 + (-14)$
Find x Value: Perform the addition to find the value of x. $\newline$ $-9x + 10x = 1x$ $\newline$ $-4y + 4y = 0y$ (which cancels out) $\newline$ $9 - 14 = -5$ $\newline$ So, $1x = -5$
Solve for x: Solve for x. $\newline$ $x = -5$
Substitute for y: Substitute the value of $x$ back into one of the original equations to find the value of $y$ . We'll use the first equation. $\newline$ $-9(-5) - 4y = 9$
Simplify Equation: Perform the multiplication to simplify the equation. $\newline$ $45 − 4y = 9$
Isolate y Term: Subtract $45$ from both sides of the equation to isolate the term containing $y$ . $\newline$ $45 - 4y - 45 = 9 - 45$ $\newline$ $-4y = -36$
Solve for y: Divide both sides by $-4$ to solve for y. $\newline$ $\frac{-4y}{-4} = \frac{-36}{-4}$ $\newline$ $y = 9$