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Solve using elimination.\newline8x−9y=−138x - 9y = -13\newline−8x+7y=19-8x + 7y = 19\newline(_____, _____)

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Q. Solve using elimination.\newline8x−9y=−138x - 9y = -13\newline−8x+7y=19-8x + 7y = 19\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline8x−9y=−138x − 9y = −13\newline−8x+7y=19−8x + 7y = 19
  2. Add Equations: Add the two equations together to eliminate the xx variable.\newline(8x−9y)+(−8x+7y)=−13+19(8x − 9y) + (−8x + 7y) = −13 + 19
  3. Eliminate xx: Perform the addition.8x−8x−9y+7y=−13+198x − 8x − 9y + 7y = −13 + 190x−2y=60x − 2y = 6
  4. Simplify Equation: Simplify the equation. −2y=6-2y = 6
  5. Solve for y: Solve for y by dividing both sides by -2＂).\(\newline\$y = \frac{6}{-2}\)\(\newline\)\(y = -3\)
  6. Substitute and Solve: Substitute \(y = -3\) into one of the original equations to solve for \(x\). We'll use the first equation.\(8x − 9(-3) = −13\)
  7. Perform Addition: Perform the multiplication and addition. \(8x + 27 = -13\)
  8. Subtract \(27\): Subtract \(27\) from both sides to solve for \(x\).\(\newline\)\(8x = -13 - 27\)
  9. Divide by \(8\): Perform the subtraction.\(\newline\)\(8x = -40\)
  10. Final Solution: Divide both sides by \(8\) to solve for \(x\).\(x = \frac{{-40}}{{8}}\)\(x = -5\)

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