Solve using elimination. –9x − 4y = 2 –9x − 7y = –10 (_____, _____)

Write Equations: Write down the system of equations. –9x − 4y = 2 –9x − 7y = –10Eliminate x: Since the coefficients of x are the same in both equations, we can eliminate x by subtracting the second equation from the first. (–9x − 4y) − (–9x − 7y) = 2 − (–10)Perform Subtraction: Perform the subtraction to eliminate x. –9x + 9x − 4y + 7y = 2 + 10Simplify Equation: Simplify the equation. 0x + 3y = 12Solve for y: Solve for y. 3y = 12 y = 12 / 3 y = 4Substitute and Solve for x: Substitute the value of y back into one of the original equations to solve for x. We can use the first equation. –9x − 4(4) = 2Finalize Solution: Simplify the equation and solve for x. –9x − 16 = 2 –9x = 2 + 16 –9x = 18 x = 18 / (–9) x = –2Write the solution as an ordered pair. The solution to the system of equations is (x, y) = (–2, 4).

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Solve using elimination. $\newline$ $-9x - 4y = 2$ $\newline$ $-9x - 7y = -10$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-9x - 4y = 2

\newline

-9x - 7y = -10

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-9x - 4y = 2$ $\newline$ $-9x - 7y = -10$
Eliminate $x$ : Since the coefficients of $x$ are the same in both equations, we can eliminate $x$ by subtracting the second equation from the first. $(–9x − 4y) − (–9x − 7y) = 2 − (–10)$
Perform Subtraction: Perform the subtraction to eliminate $x$ . $-9x + 9x - 4y + 7y = 2 + 10$
Simplify Equation: Simplify the equation. $0x + 3y = 12$
Solve for y: Solve for y. $\newline$ $3y = 12$ $\newline$ $y = \frac{12}{3}$ $\newline$ $y = 4$
Substitute and Solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the first equation. $\newline$ $−9x − 4(4) = 2$
Finalize Solution: Simplify the equation and solve for $x$ .
$–9x − 16 = 2$
$–9x = 2 + 16$
$–9x = 18$
$x = \frac{18}{(–9)}$
$x = –2$
Finalize Solution: Simplify the equation and solve for $x$ .\begin{align*} -9x - 16 &= 2\ -9x &= 2 + 16\ -9x &= 18\ x &= \frac{18}{(-9)}\ x &= -2 \end{align*}Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (-2, 4)$ .