Solve using elimination. 5x − 2y = 15 –7x + 2y = –13 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. 5x − 2y = 15 –7x + 2y = –13Add Equations: Add the two equations together to eliminate the y variable. (5x − 2y) + (–7x + 2y) = 15 + (–13)Find x: Perform the addition to find the value of x. 5x − 7x = 15 − 13 −2x = 2Solve for x: Divide both sides by -2 to solve for x. −2x / -2 = 2 / -2 x = -1Substitute x: Substitute x = -1 into one of the original equations to solve for y. We'll use the first equation. 5(-1) − 2y = 15Simplify Equation: Perform the multiplication and simplify the equation. −5 − 2y = 15Isolate y: Add 5 to both sides to isolate the term with y. −2y = 15 + 5 −2y = 20Solve for y: Divide both sides by -2 to solve for y. −2y / -2 = 20 / -2 y = -10

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Solve using elimination. $\newline$ $5x - 2y = 15$ $\newline$ $-7x + 2y = -13$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

5x - 2y = 15

\newline

-7x + 2y = -13

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $5x − 2y = 15$ $\newline$ $−7x + 2y = −13$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(5x − 2y) + (−7x + 2y) = 15 + (−13)$
Find $x$ : Perform the addition to find the value of $x$ . $5x − 7x = 15 − 13$ $−2x = 2$
Solve for x: Divide both sides by $-2$ to solve for x. $\newline$ $\frac{-2x}{-2} = \frac{2}{-2}$ $\newline$ $x = -1$
Substitute $x$ : Substitute $x = -1$ into one of the original equations to solve for $y$ . We'll use the first equation. $5(-1) − 2y = 15$
Simplify Equation: Perform the multiplication and simplify the equation. $-5 - 2y = 15$
Isolate y: Add $5$ to both sides to isolate the term with $y$ . $\newline$ $-2y = 15 + 5$ $\newline$ $-2y = 20$
Solve for y: Divide both sides by $-2$ to solve for y. $\newline$ $-2y / -2 = 20 / -2$ $\newline$ $y = -10$