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Solve using elimination.\newline9x−2y=−89x - 2y = -8\newline9x−6y=129x - 6y = 12\newline(_____, _____)

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Q. Solve using elimination.\newline9x−2y=−89x - 2y = -8\newline9x−6y=129x - 6y = 12\newline(_____, _____)
  1. Set Up Equations: First, we need to set up the equations to eliminate one of the variables. We can do this by subtracting the second equation from the first equation.\newline9x−2y=−89x − 2y = −8 (Equation 11)\newline9x−6y=129x − 6y = 12 (Equation 22)\newlineSubtract Equation 22 from Equation 11:\newline(9x−2y)−(9x−6y)=(−8)−(12)(9x − 2y) − (9x − 6y) = (−8) − (12)
  2. Subtract Equations: Now, perform the subtraction:\newline9x−9x−2y+6y=−8−129x - 9x - 2y + 6y = -8 - 12\newline0x+4y=−200x + 4y = -20\newlineThis simplifies to:\newline4y=−204y = -20
  3. Solve for y: Next, we solve for yy by dividing both sides of the equation by 44:4y4=−204\frac{4y}{4} = \frac{-20}{4}y=−5y = -5
  4. Substitute and Solve for x: Now that we have the value of yy, we can substitute it back into one of the original equations to solve for xx. We'll use Equation 11:\newline9x−2(−5)=−89x − 2(-5) = −8\newline9x+10=−89x + 10 = -8
  5. Solve for x: Subtract 1010 from both sides to solve for x:\newline9x+10−10=−8−109x + 10 - 10 = -8 - 10\newline9x=−189x = -18
  6. Final Solution: Finally, divide both sides by 99 to find the value of xx:9x9=−189\frac{9x}{9} = \frac{-18}{9}x=−2x = -2

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