Solve using elimination. –x + 9y = –17 –x + 7y = –11 (_____, _____)

Set up equations: First, we need to set up the two equations given to us: –x + 9y = –17 –x + 7y = –11 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 eliminate x by subtracting the second equation from the first.Eliminate variable: Subtract the second equation from the first: (–x + 9y) - (–x + 7y) = (–17) - (–11) This simplifies to: –x + 9y + x - 7y = –17 + 11Simplify equation: Simplify the equation by combining like terms: 0x + 2y = –6 This simplifies to: 2y = –6Solve for y: Now, solve for y by dividing both sides of the equation by 2: 2y ÷ 2 = –6 ÷ 2 y = –3Substitute y value: 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: –x + 9y = –17 Substitute y = –3 into the equation: –x + 9(–3) = –17Simplify equation: Multiply 9 by –3 to simplify the equation: –x - 27 = –17Solve for x: Now, solve for x by adding 27 to both sides of the equation: –x - 27 + 27 = –17 + 27 –x = 10Final solution: Finally, multiply both sides by -1 to solve for x: –x * -1 = 10 * -1 x = –10

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Solve using elimination. $\newline$ $-x + 9y = -17$ $\newline$ $-x + 7y = -11$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-x + 9y = -17

\newline

-x + 7y = -11

\newline

(_____, _____)

Set up equations: First, we need to set up the two equations given to us: $\newline$ $-x + 9y = -17$ $\newline$ $-x + 7y = -11$ $\newline$ 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 eliminate $x$ by subtracting the second equation from the first.
Eliminate variable: Subtract the second equation from the first: $\newline$ $(–x + 9y) - (–x + 7y) = (–17) - (–11)$ $\newline$ This simplifies to: $\newline$ $–x + 9y + x - 7y = –17 + 11$
Simplify equation: Simplify the equation by combining like terms: $\newline$ $0x + 2y = -6$ $\newline$ This simplifies to: $\newline$ $2y = -6$
Solve for y: Now, solve for y by dividing both sides of the equation by $2$ : $\newline$ $2y \div 2 = -6 \div 2$ $\newline$ $y = -3$
Substitute y value: 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: $\newline$ $-x + 9y = -17$ $\newline$ Substitute $y = -3$ into the equation: $\newline$ $-x + 9(-3) = -17$
Simplify equation: Multiply $9$ by $-3$ to simplify the equation: $\newline$ $-x - 27 = -17$
Solve for x: Now, solve for x by adding $27$ to both sides of the equation: $\newline$ $-x - 27 + 27 = -17 + 27$ $\newline$ $-x = 10$
Final solution: Finally, multiply both sides by $-1$ to solve for $x$ :$\newline$ $-x \times -1 = 10 \times -1$ $\newline$ $x = -10$