Solve using elimination. –10x + 5y = –15 –9x + 5y = –18 (_____, _____)

Write Equations: Write down the system of equations. –10x + 5y = –15 –9x + 5y = –18Eliminate y: Subtract the second equation from the first equation to eliminate the y variable. (–10x + 5y) - (–9x + 5y) = (–15) - (–18) This simplifies to: –10x + 5y + 9x - 5y = –15 + 18Combine Terms: Combine like terms. (–10x + 9x) + (5y - 5y) = –15 + 18 –1x + 0y = 3 This simplifies to: –1x = 3Solve for x: Solve for x. Divide both sides by -1 to isolate x. –1x / -1 = 3 / -1 x = –3Substitute x: Substitute x = –3 into one of the original equations to solve for y. Using the first equation: –10x + 5y = –15 Substitute x: –10(–3) + 5y = –15Simplify for y: Simplify and solve for y. 30 + 5y = –15 Subtract 30 from both sides: 5y = –15 – 30 5y = –45Find y: Divide both sides by 5 to find the value of y. 5y / 5 = –45 / 5 y = –9

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Solve using elimination. $\newline$ $-10x + 5y = -15$ $\newline$ $-9x + 5y = -18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-10x + 5y = -15

\newline

-9x + 5y = -18

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-10x + 5y = -15$ $\newline$ $-9x + 5y = -18$
Eliminate y: Subtract the second equation from the first equation to eliminate the $y$ variable. $\newline$ $(-10x + 5y) - (-9x + 5y) = (-15) - (-18)$ $\newline$ This simplifies to: $\newline$ $-10x + 5y + 9x - 5y = -15 + 18$
Combine Terms: Combine like terms. $\newline$ $(-10x + 9x) + (5y - 5y) = -15 + 18$ $\newline$ $-1x + 0y = 3$ $\newline$ This simplifies to: $\newline$ $-1x = 3$
Solve for x: Solve for x. $\newline$ Divide both sides by $-1$ to isolate $x$ . $\newline$ $\frac{-1x}{-1} = \frac{3}{-1}$ $\newline$ $x = -3$
Substitute $x$ : Substitute $x = -3$ into one of the original equations to solve for $y$ . Using the first equation: $-10x + 5y = -15$ Substitute $x$ : $-10(-3) + 5y = -15$
Simplify for $y$ : Simplify and solve for $y$ . $30 + 5y = -15$ Subtract $30$ from both sides: $5y = -15 - 30$ $5y = -45$
Find $y$ : Divide both sides by $5$ to find the value of $y$ . $\frac{5y}{5} = \frac{-45}{5}$ $y = -9$