Solve using elimination. –3x − 4y = –15 –3x − 3y = –18 (_____, _____)

Write Equations: Write down the system of equations. –3x − 4y = –15 –3x − 3y = –18Use Elimination: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of x are the same in both equations, we can subtract the second equation from the first to eliminate x. Subtract the second equation from the first: (–3x − 4y) − (–3x − 3y) = (–15) − (–18)Subtract Equations: Perform the subtraction. –3x + 3x − 4y + 3y = –15 + 18 The x terms cancel out, and we are left with: −4y + 3y = 3Combine Terms: Combine like terms. −y = 3Solve for y: Solve for y by dividing both sides by -1. y = 3 / -1 y = -3Substitute y: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation: –3x − 4y = –15 Substitute y = -3 into the equation: –3x − 4(-3) = –15Perform Multiplication: Perform the multiplication and simplify. –3x + 12 = –15Isolate x Term: Subtract 12 from both sides to isolate the term with x. –3x = –15 − 12 –3x = –27Solve for x: Divide both sides by -3 to solve for x. x = –27 / -3 x = 9

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Solve using elimination. $\newline$ $-3x - 4y = -15$ $\newline$ $-3x - 3y = -18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x - 4y = -15

\newline

-3x - 3y = -18

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-3x - 4y = -15$ $\newline$ $-3x - 3y = -18$
Use Elimination: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $x$ are the same in both equations, we can subtract the second equation from the first to eliminate $x$ .
Subtract the second equation from the first:
$(–3x − 4y) − (–3x − 3y) = (–15) − (–18)$
Subtract Equations: Perform the subtraction. $\newline$ $-3x + 3x - 4y + 3y = -15 + 18$ $\newline$ The x terms cancel out, and we are left with: $\newline$ $-4y + 3y = 3$
Combine Terms: Combine like terms. $\newline$ $-y = 3$
Solve for y: Solve for y by dividing both sides by -1＂).$\newline\$y = \frac{3}{-1}$$\newline$$y = -3$
Substitute $y$: Now that we have the value of $y$, we can substitute it back into one of the original equations to solve for $x$. Let's use the first equation:$\newline$$–3x − 4y = –15$$\newline$Substitute $y = -3$ into the equation:$\newline$$–3x − 4(-3) = –15$
Perform Multiplication: Perform the multiplication and simplify. $-3x + 12 = -15$
Isolate x Term: Subtract $12$ from both sides to isolate the term with $x$.$\newline$$-3x = -15 - 12$$\newline$$-3x = -27$
Solve for x: Divide both sides by $-3$ to solve for x.$\newline$$x = \frac{-27}{-3}$$\newline$$x = 9$