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Solve using elimination.\newline−x−9y=12-x - 9y = 12\newline2x+9y=−62x + 9y = -6\newline(_____, _____)

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Q. Solve using elimination.\newline−x−9y=12-x - 9y = 12\newline2x+9y=−62x + 9y = -6\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline−x−9y=12-x - 9y = 12\newline2x+9y=−62x + 9y = -6
  2. Add Equations: Add the two equations together to eliminate the yy variable.\newline(−x−9y)+(2x+9y)=12+(−6)(-x - 9y) + (2x + 9y) = 12 + (-6)
  3. Find xx: Perform the addition to find the value of xx.
    −x+2x=x-x + 2x = x
    −9y+9y=0-9y + 9y = 0
    12+(-6)=612 + (\text{-}6) = 6
    So, x=6x = 6
  4. Substitute xx: Substitute the value of xx back into one of the original equations to solve for yy. We can use the first equation: –x−9y=12–x − 9y = 12.\newline–(6)−9y=12–(6) − 9y = 12
  5. Solve for y: Solve for y.\newline−6−9y=12-6 - 9y = 12\newline9y=−6−129y = -6 - 12\newline9y=−189y = -18\newliney=−18÷9y = -18 \div 9\newliney=−2y = -2

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