# SOLUTION: Solve by substitution or elimination: 5x+2y+10z=5 3x-y+5z=-6 2x-3y-7z=5

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 Question 162863: Solve by substitution or elimination: 5x+2y+10z=5 3x-y+5z=-6 2x-3y-7z=5Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!``` Solve by substitution or elimination: 5x + 2y + 10z = 5 3x - y + 5z = -6 2x - 3y - 7z = 5 1. Pick a pair of equations and a letter to eliminate: I'll pick the first two equations and I'll pick y to eliminate from them: 5x + 2y + 10z = 5 3x - y + 5z = -6 I can eliminate y by multiplying the second equation through by 2 and adding vertically term by term: 5x + 2y + 10z = 5 6x - 2y + 10z = -12 -------------------- 11x + 20z = -7 2. Pick a DIFFERENT pair of equations but the SAME letter to eliminate: I'll pick the last two equations and I must eliminate y from them: 3x - y + 5z = -6 2x - 3y - 7z = 5 I can eliminate y by multiplying the upper equation through by -3 and adding vertically term by term: -9x + 3y - 15z = 18 2x - 3y - 7z = 5 ------------------- -7x - 22z = 23 Next we put those two equations in which we have eliminated y together: -7x - 22z = 23 11x + 20z = -7 We can eliminate x by multiplying the upper equation by 11 and the bottom one by 7 -77x - 242z = 253 77x + 140z = -49 ----------------- -102z = 204 z = -2 Substitute z = -2 into -7x - 22z = 23 -7x - 22(-2) = 23 -7x + 44 = 23 -7x = -21 x = 3 Substitute z = -2 and x = 3 into one of the original three equations: 3x - y + 5z = -6 3(3) - y + 5(-2) = -6 9 - y - 10 = -6 -y - 1 = -6 -y = -5 y = 5 (x, y, z) = (3, 5, -2) Edwin```