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Systems of Equations

Solve two linear equations by elimination — every step explained, with exact fraction answers.

x+y=
x+y=
  1. 1

    The system of equations.

    2x + 3y = 12

    x − y = 1

  2. 2

    Line up the y-terms: multiply equation 1 by b₂ and equation 2 by b₁.

    -2x − 3y = -12

    3x − 3y = 3

  3. 3

    Subtract the equations to eliminate y, then solve for x.

    -5x = -15

    x = 3

  4. 4

    Substitute x back in to find y.

    2x + 3y = 12 with x = 3

    y = 2

Solution

x = 3, y = 2