2x - 3y + 5z = 13 4x + 4y + 6z = 34 Since you want the y-variable by itself, get the y-terms off the left sides and onto the right side 2x + 5z = 13 + 3y 4x + 6z = 34 - 4y Eliminate x by multiplying the first equation by -2 and adding it term-by-term to the second equation: -4x - 10z = -26 - 6y 4x + 6z = 34 - 4y -------------------- -4z = 8 - 10y z =- y z = -2 + y Go back to 2x + 5z = 13 + 3y 4x + 6z = 34 - 4y Eliminate z by multiplying the first equation by -6 and the second equation by 5 -12x - 30z = -78 - 18y 20x + 30z = 170 - 20y ---------------------- 8x = 92 - 38y x = - y x = - y So the solution with y by itself is (x, y, z) = ( - y, y, -2 + y) Edwin