Solve using elimination. –5x − 7y = –19 –5x − y = –7 (_____, _____)

Write Equations: Write down the system of equations. –5x − 7y = –19 –5x − y = –7Elimination Step: In order to use elimination, we need to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. Subtracting the second equation from the first, we get: (–5x − 7y) − (–5x − y) = –19 − (–7)Perform Subtraction: Perform the subtraction. –5x + 5x − 7y + y = –19 + 7 This simplifies to: 0x − 6y = –12Solve for y: Now we have an equation with only one variable, which we can solve for y. −6y = –12 Divide both sides by -6 to find y: y = –12 / -6 y = 2Substitute and Solve: Substitute the value of y back into one of the original equations to solve for x. We can use the second equation for this purpose. –5x − y = –7 Substitute y = 2: –5x − 2 = –7Isolate x: Add 2 to both sides to isolate the term with x. –5x = –7 + 2 –5x = –5Final Solution: Divide both sides by -5 to solve for x. x = –5 / -5 x = 1

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Solve using elimination. $\newline$ $-5x - 7y = -19$ $\newline$ $-5x - y = -7$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-5x - 7y = -19

\newline

-5x - y = -7

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-5x - 7y = -19$ $\newline$ $-5x - y = -7$
Elimination Step: In order to use elimination, we need to eliminate one of the variables. We can do this by subtracting the second equation from the first equation. $\newline$ Subtracting the second equation from the first, we get: $\newline$ $(-5x - 7y) - (-5x - y) = -19 - (-7)$
Perform Subtraction: Perform the subtraction. $\newline$ $-5x + 5x - 7y + y = -19 + 7$ $\newline$ This simplifies to: $\newline$ $0x - 6y = -12$
Solve for y: Now we have an equation with only one variable, which we can solve for $y$ . $-6y = -12$ Divide both sides by $-6$ to find $y$ : $y = -12 / -6$ $y = 2$
Substitute and Solve: Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the second equation for this purpose. $\newline$ $-5x - y = -7$ $\newline$ Substitute $y = 2$ : $\newline$ $-5x - 2 = -7$
Isolate x: Add $2$ to both sides to isolate the term with $x$ . $\newline$ $-5x = -7 + 2$ $\newline$ $-5x = -5$
Final Solution: Divide both sides by $-5$ to solve for $x$ . $x = \frac{-5}{-5}$ $x = 1$