Solve using elimination. –4x − 6y = –10 7x + 6y = –5 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –4x − 6y = –10 7x + 6y = –5Add Equations: Add the two equations together to eliminate the y variable. (–4x − 6y) + (7x + 6y) = (–10) + (–5)Find x: Perform the addition to find the value of x. –4x + 7x = 3x –6y + 6y = 0y (which cancels out) –10 + (–5) = –15 So, 3x = –15Solve for x: Solve for x by dividing both sides of the equation by 3. 3x = –15 x = –15 / 3 x = –5Substitute x: Substitute x = –5 into one of the original equations to solve for y. We'll use the first equation. –4(–5) − 6y = –10Simplify Equation: Perform the multiplication to simplify the equation. 20 − 6y = –10Isolate y: Subtract 20 from both sides of the equation to isolate the term containing y. 20 − 6y − 20 = –10 − 20 –6y = –30Solve for y: Solve for y by dividing both sides of the equation by –6. –6y = –30 y = –30 / (–6) y = 5

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Solve using elimination. $\newline$ $-4x - 6y = -10$ $\newline$ $7x + 6y = -5$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-4x - 6y = -10

\newline

7x + 6y = -5

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-4x - 6y = -10$ $\newline$ $7x + 6y = -5$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-4x - 6y) + (7x + 6y) = (-10) + (-5)$
Find $x$ : Perform the addition to find the value of $x$ .
$-4x + 7x = 3x$
$-6y + 6y = 0y$ (which cancels out)
$-10 + (-5) = -15$
So, $3x = -15$
Solve for x: Solve for x by dividing both sides of the equation by $3$ . $\newline$ $3x = -15$ $\newline$ $x = -\frac{15}{3}$ $\newline$ $x = -5$
Substitute $x$ : Substitute $x = -5$ into one of the original equations to solve for $y$ . We'll use the first equation. $-4(-5) - 6y = -10$
Simplify Equation: Perform the multiplication to simplify the equation. $20 - 6y = -10$
Isolate $y$ : Subtract $20$ from both sides of the equation to isolate the term containing $y$ . $20 - 6y - 20 = -10 - 20$ $-6y = -30$
Solve for y: Solve for y by dividing both sides of the equation by $–6$ . $\newline$ $–6y = –30$ $\newline$ $y = \frac{–30}{(–6)}$ $\newline$ $y = 5$