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What is the point of intersection of the lines x + y = 5 and 2x - y = 1?

Practice Questions

Q1
What is the point of intersection of the lines x + y = 5 and 2x - y = 1?
  1. (2, 3)
  2. (3, 2)
  3. (1, 4)
  4. (4, 1)

Questions & Step-by-Step Solutions

What is the point of intersection of the lines x + y = 5 and 2x - y = 1?
  • Step 1: Write down the two equations: x + y = 5 and 2x - y = 1.
  • Step 2: Solve the first equation for y: y = 5 - x.
  • Step 3: Substitute y in the second equation: 2x - (5 - x) = 1.
  • Step 4: Simplify the equation: 2x - 5 + x = 1.
  • Step 5: Combine like terms: 3x - 5 = 1.
  • Step 6: Add 5 to both sides: 3x = 6.
  • Step 7: Divide both sides by 3: x = 2.
  • Step 8: Substitute x back into the first equation to find y: y = 5 - 2.
  • Step 9: Calculate y: y = 3.
  • Step 10: Write the point of intersection as (x, y): The point of intersection is (2, 3).
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