The Math Meridian
Back to Grade 8

Systems with three variables

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Learn it Use one equation to eliminate the same variable (say x) from the other two. That leaves two equations in y and z: solve those, then substitute back to find x.

Example: $x + y + z = 6$, $2x - y + z = 3$, $x + 2y - z = 2$

  1. Eliminate z. Eq 1 + Eq 3: $2x + 3y = 8$. Eq 2 + Eq 3: $3x + y = 5$.
  2. Solve these two: $y = 5 - 3x$, so $2x + 15 - 9x = 8$, $x = 1$, $y = 2$.
  3. Back in Eq 1: $1 + 2 + z = 6$, $z = 3$. Solution $(1, 2, 3)$.

Loading questions…