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What is the solution set of the system of equations: x + y = 5 and x - y = 1?

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Question: What is the solution set of the system of equations: x + y = 5 and x - y = 1?

Options:

  1. (2, 3)
  2. (3, 2)
  3. (1, 4)
  4. (4, 1)

Correct Answer: (2, 3)

Solution: 

Solving the system gives x = 2 and y = 3, thus the solution set is (2, 3).

What is the solution set of the system of equations: x + y = 5 and x - y = 1?

Practice Questions

Q1
What is the solution set of the system of equations: x + y = 5 and x - y = 1?
  1. (2, 3)
  2. (3, 2)
  3. (1, 4)
  4. (4, 1)

Questions & Step-by-Step Solutions

What is the solution set of the system of equations: x + y = 5 and x - y = 1?
  • Step 1: Write down the two equations: x + y = 5 and x - y = 1.
  • Step 2: Solve the first equation for y: y = 5 - x.
  • Step 3: Substitute y in the second equation: x - (5 - x) = 1.
  • Step 4: Simplify the equation: x - 5 + x = 1, which becomes 2x - 5 = 1.
  • Step 5: Add 5 to both sides: 2x = 6.
  • Step 6: Divide both sides by 2: x = 3.
  • Step 7: Substitute x back into the first equation to find y: 3 + y = 5.
  • Step 8: Solve for y: y = 5 - 3, which gives y = 2.
  • Step 9: The solution is (x, y) = (3, 2).
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