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Solve using elimination.\newline−x+9y=−9-x + 9y = -9\newlinex+4y=−17x + 4y = -17\newline(_____, _____)

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Q. Solve using elimination.\newline−x+9y=−9-x + 9y = -9\newlinex+4y=−17x + 4y = -17\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline−x+9y=−9-x + 9y = -9\newlinex+4y=−17x + 4y = -17
  2. Add Equations: Add the two equations together to eliminate xx.(−x+9y)+(x+4y)=(−9)+(−17)\left( -x + 9y \right) + \left( x + 4y \right) = \left( -9 \right) + \left( -17 \right)
  3. Combine Terms: Perform the addition to eliminate xx and combine like terms. −x+x+9y+4y=−9−17\,-x + x + 9y + 4y = -9 - 17 0x+13y=−26\,0x + 13y = -26
  4. Solve for y: Solve for y.\newline13y=−2613y = -26\newliney=−2613y = -\frac{26}{13}\newliney=−2y = -2
  5. Substitute and Solve: Substitute y=−2y = -2 into one of the original equations to solve for xx. We'll use the second equation: x+4y=−17x + 4y = -17.\newlinex+4(−2)=−17x + 4(-2) = -17
  6. Final Solution: Perform the multiplication and solve for xx.x−8=−17x - 8 = -17x=−17+8x = -17 + 8x=−9x = -9

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