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What is the solution set of the equations x + y = 10 and x - y = 2? (2023)

Practice Questions

Q1
What is the solution set of the equations x + y = 10 and x - y = 2? (2023)
  1. (6, 4)
  2. (8, 2)
  3. (5, 5)
  4. (7, 3)

Questions & Step-by-Step Solutions

What is the solution set of the equations x + y = 10 and x - y = 2? (2023)
  • Step 1: Write down the two equations: x + y = 10 and x - y = 2.
  • Step 2: Solve the second equation (x - y = 2) for x: x = y + 2.
  • Step 3: Substitute the expression for x from Step 2 into the first equation: (y + 2) + y = 10.
  • Step 4: Combine like terms: 2y + 2 = 10.
  • Step 5: Subtract 2 from both sides: 2y = 8.
  • Step 6: Divide both sides by 2: y = 4.
  • Step 7: Now that we have y, substitute y back into the expression for x: x = 4 + 2.
  • Step 8: Calculate x: x = 6.
  • Step 9: The solution set is (x, y) = (6, 4).
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