Solve using elimination. –4x + 6y = 6 7x − 6y = 12 (_____, _____)

Write Equations: Write down the system of equations. –4x + 6y = 6 7x − 6y = 12 We need to eliminate one of the variables by adding the two equations together.Add Equations: Add the two equations together to eliminate y. (–4x + 6y) + (7x − 6y) = 6 + 12 The y terms cancel each other out, leaving us with: –4x + 7x = 18Combine Terms: Combine like terms to solve for x. –4x + 7x = 3x 3x = 18Solve for x: Divide both sides by 3 to find the value of x. 3x / 3 = 18 / 3 x = 6Substitute x: Substitute x = 6 into one of the original equations to solve for y. We'll use the first equation. –4(6) + 6y = 6 –24 + 6y = 6Isolate y: Add 24 to both sides to isolate the y term. 6y = 6 + 24 6y = 30Solve for y: Divide both sides by 6 to find the value of y. 6y / 6 = 30 / 6 y = 5

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Solve using elimination. $\newline$ $-4x + 6y = 6$ $\newline$ $7x - 6y = 12$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-4x + 6y = 6

\newline

7x - 6y = 12

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-4x + 6y = 6$ $\newline$ $7x − 6y = 12$ $\newline$ We need to eliminate one of the variables by adding the two equations together.
Add Equations: Add the two equations together to eliminate $y$ . $\newline$ $(-4x + 6y) + (7x − 6y) = 6 + 12$ $\newline$ The $y$ terms cancel each other out, leaving us with: $\newline$ $−4x + 7x = 18$
Combine Terms: Combine like terms to solve for $x$ . $\,-4x + 7x = 3x$ $\,3x = 18$
Solve for x: Divide both sides by $3$ to find the value of x. $\newline$ $\frac{3x}{3} = \frac{18}{3}$ $\newline$ $x = 6$
Substitute $x$ : Substitute $x = 6$ into one of the original equations to solve for $y$ . We'll use the first equation. $\newline$ $-4(6) + 6y = 6$ $\newline$ $-24 + 6y = 6$
Isolate $y$ : Add $24$ to both sides to isolate the $y$ term. $\newline$ $6y = 6 + 24$ $\newline$ $6y = 30$
Solve for y: Divide both sides by $6$ to find the value of y. $\newline$ $\frac{6y}{6} = \frac{30}{6}$ $\newline$ $y = 5$