Simultaneous Equations

Solve pairs of linear equations using elimination or substitution, then verify the shared solution.

Curriculum rangeYears 9–11

When both equations have the same y-coefficient, subtracting one from the other eliminates y in a single step.

Solution x

Solution y

Eq.1 x-coeff

Eq.2 x-coeff

Shared y-coeff

$2x + 3y = 12$ — equation 1

$5x + 3y = 21$ — equation 2

Step 1 — subtract equation 2 from equation 1 (the y-terms cancel):

$-3x = -9$

$x = -9 \div -3 = 3$

Step 2 — substitute x = 3 back into equation 1 to find y:

$2(3) + 3y = 12$

$x = 3, \ y = 2$