Solve using elimination. –3x − 4y = 7 6x + 4y = 14 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –3x − 4y = 7 6x + 4y = 14Add Equations: Add the two equations together to eliminate the y variable. (–3x − 4y) + (6x + 4y) = 7 + 14Perform Addition: Perform the addition to see the result. –3x + 6x = 3x and −4y + 4y = 0, so we are left with 3x = 21.Solve for x: Solve for x by dividing both sides of the equation by 3. 3x ÷ 3 = 21 ÷ 3 x = 7Substitute x: Substitute x = 7 into one of the original equations to solve for y. We can use the first equation –3x − 4y = 7. –3(7) − 4y = 7Perform Subtraction: Perform the multiplication and subtraction to isolate the y variable. –21 − 4y = 7Add 21: Add 21 to both sides of the equation to solve for y. –4y = 7 + 21 –4y = 28Divide by -4: Divide both sides by -4 to find the value of y. –4y ÷ (–4) = 28 ÷ (–4) y = –7

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Solve using elimination. $\newline$ $-3x - 4y = 7$ $\newline$ $6x + 4y = 14$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x - 4y = 7

\newline

6x + 4y = 14

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-3x - 4y = 7$ $\newline$ $6x + 4y = 14$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-3x - 4y) + (6x + 4y) = 7 + 14$
Perform Addition: Perform the addition to see the result. $\newline$ $-3x + 6x = 3x$ and $-4y + 4y = 0$ , so we are left with $3x = 21$ .
Solve for x: Solve for x by dividing both sides of the equation by $3$ . $\newline$ $3x \div 3 = 21 \div 3$ $\newline$ $x = 7$
Substitute $x$ : Substitute $x = 7$ into one of the original equations to solve for $y$ . We can use the first equation $–3x − 4y = 7$ . $\newline$ $–3(7) − 4y = 7$
Perform Subtraction: Perform the multiplication and subtraction to isolate the $y$ variable. $\,-21 - 4y = 7$
Add $21$ : Add $21$ to both sides of the equation to solve for $y$ .
$-4y = 7 + 21$
$-4y = 28$
Divide by $-4$ : Divide both sides by $-4$ to find the value of $y$ .-4y \div (\-4) = 28 \div (\-4)y = \-7