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Solve using elimination.\newline9x−7y=−169x - 7y = -16\newline−10x+7y=10-10x + 7y = 10\newline(_____, _____)

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Q. Solve using elimination.\newline9x−7y=−169x - 7y = -16\newline−10x+7y=10-10x + 7y = 10\newline(_____, _____)
  1. Write Equations: Write down the system of equations to be solved using elimination.\newline9x−7y=−169x − 7y = −16\newline−10x+7y=10−10x + 7y = 10
  2. Add Equations: Add the two equations together to eliminate the yy variable.\newline(9x−7y)+(−10x+7y)=(−16)+(10)(9x − 7y) + (−10x + 7y) = (−16) + (10)
  3. Find xx: Perform the addition to find the value of xx.9x−10x=−16+109x − 10x = −16 + 10−1x=−6−1x = −6x=6x = 6
  4. Substitute xx: Substitute the value of xx back into one of the original equations to solve for yy. We'll use the first equation.9(6)−7y=−169(6) − 7y = −1654−7y=−1654 − 7y = −16
  5. Isolate y: Isolate the yy variable by subtracting 5454 from both sides of the equation.\newline−7y=−16−54−7y = −16 − 54\newline−7y=−70−7y = −70\newliney=10y = 10
  6. Check Solution: Check the solution by substituting both xx and yy values into the second original equation.\(\newline\)−10(6)+7(10)=10-10(6) + 7(10) = 10\(\newline\)−60+70=10-60 + 70 = 10\(\newline\)10=1010 = 10\(\newline\)The solution checks out.

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