Solve using elimination. –5x + 7y = 20 5x − 3y = 20 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –5x + 7y = 20 5x − 3y = 20Add Equations: Add the two equations together to eliminate the x variable. (–5x + 7y) + (5x − 3y) = 20 + 20Perform Addition: Perform the addition to eliminate the x variable. –5x + 5x + 7y − 3y = 40 0x + 4y = 40Simplify Equation: Simplify the resulting equation. 4y = 40Divide for y: Divide both sides of the equation by 4 to solve for y. 4y ÷ 4 = 40 ÷ 4 y = 10Substitute for x: Substitute y = 10 back into one of the original equations to solve for x. We can use the second equation for this purpose. 5x − 3(10) = 20Simplify Equation: Perform the multiplication and simplify the equation. 5x − 30 = 20Isolate x: Add 30 to both sides of the equation to isolate the x term. 5x − 30 + 30 = 20 + 30 5x = 50Divide for x: Divide both sides of the equation by 5 to solve for x. 5x ÷ 5 = 50 ÷ 5 x = 10

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Solve using elimination. $\newline$ $-5x + 7y = 20$ $\newline$ $5x - 3y = 20$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-5x + 7y = 20

\newline

5x - 3y = 20

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-5x + 7y = 20$ $\newline$ $5x - 3y = 20$
Add Equations: Add the two equations together to eliminate the $x$ variable. $\newline$ $(-5x + 7y) + (5x − 3y) = 20 + 20$
Perform Addition: Perform the addition to eliminate the $x$ variable. $\,-5x + 5x + 7y − 3y = 40$ $\,0x + 4y = 40$
Simplify Equation: Simplify the resulting equation. $\newline$ $4y = 40$
Divide for $y$ : Divide both sides of the equation by $4$ to solve for $y$ . $4y \div 4 = 40 \div 4$ $y = 10$
Substitute for x: Substitute $y = 10$ back into one of the original equations to solve for $x$ . We can use the second equation for this purpose. $\newline$ $5x − 3(10) = 20$
Simplify Equation: Perform the multiplication and simplify the equation. $5x - 30 = 20$
Isolate x: Add $30$ to both sides of the equation to isolate the $x$ term. $\newline$ $5x - 30 + 30 = 20 + 30$ $\newline$ $5x = 50$
Divide for x: Divide both sides of the equation by $5$ to solve for x. $\newline$ $5x \div 5 = 50 \div 5$ $\newline$ $x = 10$