Solve using elimination. –3x − 8y = 13 –5x − 8y = –5 (_____, _____)

Write Equations: Write down the system of equations. –3x − 8y = 13 –5x − 8y = –5Eliminate y: Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the second equation from the first. (–3x − 8y) − (–5x − 8y) = 13 − (–5)Perform Subtraction: Perform the subtraction. –3x + 5x − 8y + 8y = 13 + 5Simplify Equation: Simplify the equation. 2x = 18Solve for x: Solve for x by dividing both sides by 2. x = 18 / 2 x = 9Substitute x into Equation: Substitute x = 9 into one of the original equations to solve for y. We'll use the first equation. –3(9) − 8y = 13Perform Multiplication: Perform the multiplication. –27 − 8y = 13Add 27: Add 27 to both sides to isolate the term with y. –8y = 13 + 27Simplify Equation: Simplify the equation. –8y = 40Solve for y: Solve for y by dividing both sides by -8. y = 40 / (–8) y = –5

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Solve using elimination. $\newline$ $-3x - 8y = 13$ $\newline$ $-5x - 8y = -5$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x - 8y = 13

\newline

-5x - 8y = -5

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-3x - 8y = 13$ $\newline$ $-5x - 8y = -5$
Eliminate y: Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the second equation from the first. $\newline$ $(–3x − 8y) − (–5x − 8y) = 13 − (–5)$
Perform Subtraction: Perform the subtraction. $-3x + 5x - 8y + 8y = 13 + 5$
Simplify Equation: Simplify the equation. $2x = 18$
Solve for x: Solve for x by dividing both sides by $2$ . $x = \frac{18}{2}$ $x = 9$
Substitute $x$ into Equation: Substitute $x = 9$ into one of the original equations to solve for $y$ . We'll use the first equation. $\newline$ $–3(9) − 8y = 13$
Perform Multiplication: Perform the multiplication. $-27 - 8y = 13$
Add $27$ : Add $27$ to both sides to isolate the term with $y$ . $\newline$ $-8y = 13 + 27$
Simplify Equation: Simplify the equation. $-8y = 40$
Solve for y: Solve for y by dividing both sides by -8＂).$\newline\$y = \frac{40}{(\text{–}8)}$$\newline$$y = \text{–}5$