Pick two pairs: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Eliminate the same variable from each system: 4x - 3y + z = - 10. 2x + y + 3z = 0. ... Solve the system of the two new equations: -5y - 5z = - 10. 5y - 7z = 34. ... Substitute into one of the original equations: - x + 2y - 5z = 17. ... Check: Does 2(1) + 4 + 3(- 2) = 0 ? Yes.