Solve using elimination. 9x − 2y = –8 9x − 6y = 12 (_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. 9x − 2y = –8 (Equation 1) 9x − 6y = 12 (Equation 2) Subtract Equation 2 from Equation 1: (9x − 2y) − (9x − 6y) = (–8) − (12)Subtract Equations: Now, perform the subtraction: 9x - 9x - 2y + 6y = -8 - 12 0x + 4y = -20 This simplifies to: 4y = -20Solve for y: Next, we solve for y by dividing both sides of the equation by 4: 4y / 4 = -20 / 4 y = -5Substitute and Solve for x: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. We'll use Equation 1: 9x − 2(-5) = –8 9x + 10 = -8Solve for x: Subtract 10 from both sides to solve for x: 9x + 10 - 10 = -8 - 10 9x = -18Final Solution: Finally, divide both sides by 9 to find the value of x: 9x / 9 = -18 / 9 x = -2

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Solve using elimination. $\newline$ $9x - 2y = -8$ $\newline$ $9x - 6y = 12$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

9x - 2y = -8

\newline

9x - 6y = 12

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. $\newline$ $9x − 2y = −8$ (Equation $1$ ) $\newline$ $9x − 6y = 12$ (Equation $2$ ) $\newline$ Subtract Equation $2$ from Equation $1$ : $\newline$ $(9x − 2y) − (9x − 6y) = (−8) − (12)$
Subtract Equations: Now, perform the subtraction: $\newline$ $9x - 9x - 2y + 6y = -8 - 12$ $\newline$ $0x + 4y = -20$ $\newline$ This simplifies to: $\newline$ $4y = -20$
Solve for y: Next, we solve for $y$ by dividing both sides of the equation by $4$ : $\frac{4y}{4} = \frac{-20}{4}$ $y = -5$
Substitute and Solve for x: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . We'll use Equation $1$ : $\newline$ $9x − 2(-5) = −8$ $\newline$ $9x + 10 = -8$
Solve for x: Subtract $10$ from both sides to solve for x: $\newline$ $9x + 10 - 10 = -8 - 10$ $\newline$ $9x = -18$
Final Solution: Finally, divide both sides by $9$ to find the value of $x$ : $\frac{9x}{9} = \frac{-18}{9}$ $x = -2$