Solve using elimination. –7x + 9y = 20 –8x + 9y = 19 (_____, _____)

Write Equations: Write down the system of equations. –7x + 9y = 20 –8x + 9y = 19Elimination Step: 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, we can subtract the second equation from the first. Subtract the second equation from the first: (–7x + 9y) - (–8x + 9y) = 20 - 19Subtract Equations: Perform the subtraction to eliminate y. –7x + 9y - (–8x) - 9y = 20 - 19 –7x + 9y + 8x - 9y = 1Combine Terms: Combine like terms. (–7x + 8x) + (9y - 9y) = 1 x = 1Substitute x: Now that we have the value of x, we can substitute it into one of the original equations to find the value of y. Let's use the first equation. –7(1) + 9y = 20Solve for y: Solve for y. –7 + 9y = 20 9y = 20 + 7 9y = 27Find y: Divide both sides by 9 to find y. 9y ÷ 9 = 27 ÷ 9 y = 3

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Solve using elimination. $\newline$ $-7x + 9y = 20$ $\newline$ $-8x + 9y = 19$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-7x + 9y = 20

\newline

-8x + 9y = 19

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-7x + 9y = 20$ $\newline$ $-8x + 9y = 19$
Elimination Step: 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, we can subtract the second equation from the first. $\newline$ Subtract the second equation from the first: $\newline$ $(–7x + 9y) - (–8x + 9y) = 20 - 19$
Subtract Equations: Perform the subtraction to eliminate $y$ . $\newline$ $-7x + 9y - (\text{-}8x) - 9y = 20 - 19$ $\newline$ $-7x + 9y + 8x - 9y = 1$
Combine Terms: Combine like terms. $\newline$ $(-7x + 8x) + (9y - 9y) = 1$ $\newline$ $x = 1$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it into one of the original equations to find the value of $y$ . Let's use the first equation. $\newline$ $–7(1) + 9y = 20$
Solve for y: Solve for y. $\newline$ $-7 + 9y = 20$ $\newline$ $9y = 20 + 7$ $\newline$ $9y = 27$
Find $y$ : Divide both sides by $9$ to find $y$ . $\newline$ $\frac{9y}{9} = \frac{27}{9}$ $\newline$ $y = 3$