Three equations and three unknowns is two equations and two unknowns with one more step in front. These free printable worksheets give three equations in x, y and z with room to work, and an answer sheet that shows every step.
If they get stuck
The answer key prints on a separate page.
The plan never changes. Take one letter out of two different pairs of equations, which leaves two equations in two letters. Solve those the way a student already knows how. Then put the values back to find the letter removed at the start. Numbering the equations (1), (2) and (3) keeps the page readable, since each new line can say where it came from.
Every answer is a whole number and the numbers stay manageable, so the challenge is organization rather than arithmetic. The most common error is using the same pair twice, which leaves two equations that cannot finish the job. The two pairs have to bring in all three of the original equations.
x + y − 2z = −3; −3x + y − z = 0; 3x − y + 2z = 3