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x+2y=5x + 2y = 5 3x−y=13x - y = 1

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Full solution

Q. x+2y=5x + 2y = 5 3x−y=13x - y = 1
  1. Solve for x: Let's solve the first equation for x.\newlinex=5−2yx = 5 - 2y
  2. Substitute xx in second equation: Now substitute xx in the second equation with the expression we found.3(5−2y)−y=13(5 - 2y) - y = 1
  3. Expand and simplify: Let's expand and simplify. 15−6y−y=115 - 6y - y = 1
  4. Combine like terms: Combine like terms.\newline15−7y=115 - 7y = 1
  5. Subtract 1515 from both sides: Subtract 1515 from both sides.\newline−7y=1−15-7y = 1 - 15
  6. Divide by −7-7 to find yy: Simplify the right side.\newline−7y=−14-7y = -14
  7. Calculate yy: Divide both sides by −7-7 to find yy.\newliney=−14−7y = \frac{-14}{-7}
  8. Plug yy back in first equation: Calculate yy.\newliney=2y = 2
  9. Simplify right side: Now plug yy back into the first equation to find xx.\newlinex=5−2(2)x = 5 - 2(2)
  10. Calculate xx: Simplify the right side.x=5−4x = 5 - 4
  11. Calculate xx: Simplify the right side.x=5−4x = 5 - 4Calculate xx.x=1x = 1

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