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Solve using elimination.\newline10x−4y=1410x - 4y = 14\newline10x−7y=−1310x - 7y = -13\newline(_____, _____)

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Q. Solve using elimination.\newline10x−4y=1410x - 4y = 14\newline10x−7y=−1310x - 7y = -13\newline(_____, _____)
  1. Write Equations: Write down the system of equations.\newline10x−4y=1410x − 4y = 14\newline10x−7y=−1310x − 7y = −13
  2. Eliminate Variable xx: Subtract the second equation from the first equation to eliminate the variable xx.(10x−4y)−(10x−7y)=14−(−13)(10x − 4y) − (10x − 7y) = 14 − (−13)
  3. Simplify Equation: Perform the subtraction.\newline10x−10x−4y+7y=14+1310x - 10x - 4y + 7y = 14 + 13\newline0x+3y=270x + 3y = 27
  4. Solve for y: Simplify the equation. 3y=273y = 27
  5. Substitute and Solve for x: Divide both sides by 33 to solve for y.\newliney = 27÷327 \div 3\newliney = 99
  6. Perform Subtraction: Substitute y=9y = 9 into one of the original equations to solve for xx. Using the first equation: 10x−4y=1410x − 4y = 14 10x−4(9)=1410x − 4(9) = 14
  7. Isolate x: Perform the multiplication and subtraction to isolate x.\newline10x−36=1410x - 36 = 14\newline10x=14+3610x = 14 + 36\newline10x=5010x = 50
  8. Solve for x: Divide both sides by 1010 to solve for x.\newlinex=5010x = \frac{50}{10}\newlinex=5x = 5

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