Solve using elimination. –6x + 3y = 18 2x − 3y = 10 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –6x + 3y = 18 2x − 3y = 10Add Equations: Add the two equations together to eliminate the y variable. (–6x + 3y) + (2x − 3y) = 18 + 10Find x: Perform the addition to find the value of x. –6x + 2x = –4x 3y − 3y = 0 (y terms cancel out) 18 + 10 = 28 So, –4x = 28Solve for x: Solve for x by dividing both sides of the equation by –4. –4x / –4 = 28 / –4 x = –7Substitute x: Substitute x = –7 into one of the original equations to find the value of y. We can use the second equation for convenience. 2x − 3y = 10 2(–7) − 3y = 10Simplify Equation: Perform the multiplication to simplify the equation. –14 − 3y = 10Isolate y: Add 14 to both sides of the equation to isolate the term with y. –14 + 14 − 3y = 10 + 14 –3y = 24Solve for y: Solve for y by dividing both sides of the equation by –3. –3y / –3 = 24 / –3 y = –8

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Solve using elimination. $\newline$ $-6x + 3y = 18$ $\newline$ $2x - 3y = 10$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-6x + 3y = 18

\newline

2x - 3y = 10

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-6x + 3y = 18$ $\newline$ $2x - 3y = 10$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(–6x + 3y) + (2x − 3y) = 18 + 10$
Find x: Perform the addition to find the value of $x$ . $-6x + 2x = -4x$ $3y - 3y = 0$ ( $y$ terms cancel out) $18 + 10 = 28$ So, $-4x = 28$
Solve for x: Solve for x by dividing both sides of the equation by $–4$ . $\frac{–4x}{–4} = \frac{28}{–4}$ $x = –7$
Substitute $x$ : Substitute $x = -7$ into one of the original equations to find the value of $y$ . We can use the second equation for convenience. $\newline$ $2x - 3y = 10$ $\newline$ $2(-7) - 3y = 10$
Simplify Equation: Perform the multiplication to simplify the equation. $\newline$ $-14 - 3y = 10$
Isolate y: Add $14$ to both sides of the equation to isolate the term with $y$ . $\newline$ $-14 + 14 - 3y = 10 + 14$ $\newline$ $-3y = 24$
Solve for y: Solve for y by dividing both sides of the equation by $–3$ . $\frac{–3y}{–3} = \frac{24}{–3}$ $y = –8$