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Solve using elimination.\newlinex+5y=−12x + 5y = -12\newlinex−4y=−3x - 4y = -3\newline(_____, _____)

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Q. Solve using elimination.\newlinex+5y=−12x + 5y = -12\newlinex−4y=−3x - 4y = -3\newline(_____, _____)
  1. Align Equations for Elimination: Align the equations for elimination.\newlineGiven equations:\newline11) x+5y=−12x + 5y = -12\newline22) x−4y=−3x - 4y = -3\newlineWe aim to eliminate xx by making the coefficients of xx equal in both equations.
  2. Multiply Equations for Alignment: Multiply the first equation by 11 and the second equation by −1-1 to align the coefficients of xx for elimination.\newline11) x+5y=−12x + 5y = -12 (multiplied by 11)\newline22) −x+4y=3-x + 4y = 3 (multiplied by −1-1)\newlineNow, add these two equations together.
  3. Add Modified Equations: Add the modified equations.\newline(x+5y)+(−x+4y)=−12+3(x + 5y) + (-x + 4y) = -12 + 3\newlineCombine like terms:\newline5y+4y=−95y + 4y = -9\newline9y=−99y = -9\newlineNow, solve for y by dividing both sides by 99.\newliney=−9/9y = -9 / 9\newliney=−1y = -1
  4. Solve for yy: Substitute y=−1y = -1 back into one of the original equations to find xx. Use the first equation: x+5(−1)=−12x + 5(-1) = -12 x−5=−12x - 5 = -12 Now, solve for xx by adding 55 to both sides. x=−12+5x = -12 + 5 x=−7x = -7

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