Lesson 6 of 8

Systems of Equations

A system is two equations with two variables. The solution is the (x, y) point that makes BOTH true at once, which is where the two lines cross. There are two main ways to solve.

Substitution

  1. 1Solve y = x + 1 and 2x + y = 7
  2. 2Substitute x + 1 in for y: 2x + (x + 1) = 7
  3. 3Combine and solve: 3x + 1 = 7, so 3x = 6, x = 2
  4. 4Plug back in: y = 2 + 1 = 3. Solution is (2, 3)

Elimination

  1. 1Solve x + y = 6 and x - y = 2
  2. 2Add the two equations to cancel y: 2x = 8, so x = 4
  3. 3Plug into either equation: 4 + y = 6, so y = 2. Solution is (4, 2)

ON THE TEST

Use substitution when one variable is already alone (like y = ...). Use elimination when adding or subtracting will cancel a variable. Both should give the same answer.

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