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

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Q. Solve using elimination.\newline−x+9y=−17-x + 9y = -17\newline−x+7y=−11-x + 7y = -11\newline(_____, _____)
  1. Set up equations: First, we need to set up the two equations given to us:\newline−x+9y=−17-x + 9y = -17\newline−x+7y=−11-x + 7y = -11\newlineWe want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of xx are the same in both equations, we can eliminate xx by subtracting the second equation from the first.
  2. Eliminate variable: Subtract the second equation from the first:\newline(–x+9y)−(–x+7y)=(–17)−(–11)(–x + 9y) - (–x + 7y) = (–17) - (–11)\newlineThis simplifies to:\newline–x+9y+x−7y=–17+11–x + 9y + x - 7y = –17 + 11
  3. Simplify equation: Simplify the equation by combining like terms:\newline0x+2y=−60x + 2y = -6\newlineThis simplifies to:\newline2y=−62y = -6
  4. Solve for y: Now, solve for y by dividing both sides of the equation by 22:\newline2y÷2=−6÷22y \div 2 = -6 \div 2\newliney=−3y = -3
  5. 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-x + 9y = -17\newlineSubstitute y=−3y = -3 into the equation:\newline−x+9(−3)=−17-x + 9(-3) = -17
  6. Simplify equation: Multiply 99 by −3-3 to simplify the equation:\newline−x−27=−17-x - 27 = -17
  7. Solve for x: Now, solve for x by adding 2727 to both sides of the equation:\newline−x−27+27=−17+27-x - 27 + 27 = -17 + 27\newline−x=10-x = 10
  8. Final solution: Finally, multiply both sides by −1-1 to solve for xx:\(\newline\)−x×−1=10×−1-x \times -1 = 10 \times -1\(\newline\)x=−10x = -10

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