Solving the System x + y + z = 6, 2x - y + z = ...

Algebra 2 · Axiom Academy

Solve a 3-by-3 linear system by strategically eliminating one variable at a time. Solve the system of equations for x , y , and z using the elimination method: Nice work — you solved a system of three linear equations using the elimination method. The pieces worth keeping: Choose strategically: pick the variable whose coefficients are matching or exactly opposite across the equations — it cancels in a single step (here, z : +1,+1,-1 ). Eliminate systematically: eliminate the SAME variable from two different pairs of equations to collapse three unknowns into two. Reduce and solve: the resulting system solves by the same elimination (or substitution) technique. Back-substitute: plug each found value into an earlier equation to peel off the next unknown. Always verify: substitute the full solution into all three ORIGINAL equations. This elimination strategy generalizes to any number of equations and unknowns — always look for the variable that cancels most easily first.

This is the written version of the interactive lesson above. See the full Algebra 2 course.