Solve using elimination. –3x + 3y = –18 5x + 3y = 14 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –3x + 3y = –18 5x + 3y = 14Eliminate Variable: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the second equation from the first. (–3x + 3y) - (5x + 3y) = (–18) - (14)Subtract Equations: Perform the subtraction to eliminate y. –3x + 3y - 5x - 3y = –18 - 14 Combine like terms. –3x - 5x + 3y - 3y = –18 - 14Simplify Equation: Simplify the equation. –8x = –32Solve for x: Solve for x by dividing both sides of the equation by –8. x = –32 / –8 x = 4Substitute x: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation. –3(4) + 3y = –18Simplify Equation: Perform the multiplication and simplify the equation. –12 + 3y = –18Isolate y: Add 12 to both sides of the equation to isolate the term with y. 3y = –18 + 12 3y = –6Solve for y: Divide both sides of the equation by 3 to solve for y. y = –6 / 3 y = –2

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Solve using elimination. $\newline$ $-3x + 3y = -18$ $\newline$ $5x + 3y = 14$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x + 3y = -18

\newline

5x + 3y = 14

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-3x + 3y = -18$ $\newline$ $5x + 3y = 14$
Eliminate Variable: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $y$ are the same in both equations, we can eliminate $y$ by subtracting the second equation from the first. $(–3x + 3y) - (5x + 3y) = (–18) - (14)$
Subtract Equations: Perform the subtraction to eliminate $y$ . $-3x + 3y - 5x - 3y = -18 - 14$ Combine like terms. $-3x - 5x + 3y - 3y = -18 - 14$
Simplify Equation: Simplify the equation. $-8x = -32$
Solve for x: Solve for x by dividing both sides of the equation by $–8$ . $x = \frac{–32}{–8}$ $x = 4$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the first equation. $\newline$ $–3(4) + 3y = –18$
Simplify Equation: Perform the multiplication and simplify the equation. $-12 + 3y = -18$
Isolate y: Add $12$ to both sides of the equation to isolate the term with $y$ . $\newline$ $3y = -18 + 12$ $\newline$ $3y = -6$
Solve for y: Divide both sides of the equation by $3$ to solve for y. $\newline$ $y = \frac{-6}{3}$ $\newline$ $y = -2$