Solve using elimination. 9x + 7y = 6 3x + 7y = –12 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 9x + 7y = 6 3x + 7y = –12Eliminate Variable: To use elimination, we want to eliminate one of the variables by subtracting one equation from the other. Since the coefficients of y are the same in both equations, we can subtract the second equation from the first to eliminate y. (9x + 7y) - (3x + 7y) = 6 - (–12)Solve for x: Perform the subtraction to eliminate y and solve for x. 9x - 3x + 7y - 7y = 6 + 12 6x = 18Substitute x: Divide both sides of the equation by 6 to solve for x. 6x / 6 = 18 / 6 x = 3Solve for y: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation. 3x + 7y = –12 3(3) + 7y = –12Final Solution: Perform the multiplication and simplify the equation. 9 + 7y = –12 7y = –12 - 9 7y = –21Divide both sides of the equation by 7 to solve for y. 7y / 7 = –21 / 7 y = –3

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Solve using elimination. $\newline$ $9x + 7y = 6$ $\newline$ $3x + 7y = -12$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

9x + 7y = 6

\newline

3x + 7y = -12

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $9x + 7y = 6$ $\newline$ $3x + 7y = -12$
Eliminate Variable: To use elimination, we want to eliminate one of the variables by subtracting one equation from the other. Since the coefficients of $y$ are the same in both equations, we can subtract the second equation from the first to eliminate $y$ . $(9x + 7y) - (3x + 7y) = 6 - (\text{–}12)$
Solve for x: Perform the subtraction to eliminate y and solve for x. $\newline$ $9x - 3x + 7y - 7y = 6 + 12$ $\newline$ $6x = 18$
Substitute $x$ : Divide both sides of the equation by $6$ to solve for $x$ . $\frac{6x}{6} = \frac{18}{6}$ $x = 3$
Solve for y: Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the second equation. $3x + 7y = -12$ $3(3) + 7y = -12$
Final Solution: Perform the multiplication and simplify the equation. $\newline$ $9 + 7y = -12$ $\newline$ $7y = -12 - 9$ $\newline$ $7y = -21$
Final Solution: Perform the multiplication and simplify the equation. $\newline$ $9 + 7y = -12$ $\newline$ $7y = -12 - 9$ $\newline$ $7y = -21$ Divide both sides of the equation by $7$ to solve for $y$ . $\newline$ $\frac{7y}{7} = \frac{-21}{7}$ $\newline$ $y = -3$