Solve using elimination. –10x + 5y = 10 10x − 2y = 14 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –10x + 5y = 10 10x − 2y = 14Add Equations: Add the two equations together to eliminate the x variable. (–10x + 5y) + (10x − 2y) = 10 + 14Simplify Equation: Perform the addition to eliminate the x variable and simplify the equation. –10x + 10x + 5y − 2y = 10 + 14 0x + 3y = 24Solve for y: Solve for y. 3y = 24 y = 24 / 3 y = 8Substitute for x: Substitute the value of y back into one of the original equations to solve for x. We can use the first equation: –10x + 5y = 10. –10x + 5(8) = 10 –10x + 40 = 10Solve for x: Solve for x. –10x = 10 - 40 –10x = –30 x = –30 / (–10) x = 3

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Solve using elimination. $\newline$ $-10x + 5y = 10$ $\newline$ $10x - 2y = 14$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-10x + 5y = 10

\newline

10x - 2y = 14

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-10x + 5y = 10$ $\newline$ $10x - 2y = 14$
Add Equations: Add the two equations together to eliminate the $x$ variable. $\newline$ $(-10x + 5y) + (10x − 2y) = 10 + 14$
Simplify Equation: Perform the addition to eliminate the $x$ variable and simplify the equation. $\,-10x + 10x + 5y − 2y = 10 + 14$ $\,0x + 3y = 24$
Solve for y: Solve for y. $\newline$ $3y = 24$ $\newline$ $y = \frac{24}{3}$ $\newline$ $y = 8$
Substitute for x: Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the first equation: $-10x + 5y = 10$ . $\newline$ $-10x + 5(8) = 10$ $\newline$ $-10x + 40 = 10$
Solve for x: Solve for x. $\newline$ $-10x = 10 - 40$ $\newline$ $-10x = -30$ $\newline$ $x = -30 / (-10)$ $\newline$ $x = 3$