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Solve the system y = 2x - 1 and 3x + 2y = 12

Worked through step by step. More systems.

Answer
(2,3)\boxed{(2, 3)}

Checking the result by substituting x=2x = 2 and y=3y = 3 into 3x+2y=123x + 2y = 12 gives 3(2)+2(3)=6+6=123(2) + 2(3) = 6 + 6 = 12, which is correct.

Problem: Solve the system of linear equations y=2x−1y = 2x - 1 and 3x+2y=123x + 2y = 12.

Steps

  1. Substitute the first equation into the second equation
    3x+2(2x−1)=123x + 2(2x - 1) = 12
  2. Distribute the 2
    3x+4x−2=123x + 4x - 2 = 12
  3. Combine like terms
    7x−2=127x - 2 = 12
  4. Add 2 to both sides
    7x=147x = 14
  5. Divide both sides by 7
    x=2x = 2
  6. Substitute x=2x = 2 back into the first equation to find yy
    y=2(2)−1y = 2(2) - 1
  7. Simplify the expression
    y=3y = 3

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