# SOLUTION: how do I eliminate variables using the addition method? 2x-y+z=1 3x-3y+4z=5 4x-2y+3z=4

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 Question 209868: how do I eliminate variables using the addition method? 2x-y+z=1 3x-3y+4z=5 4x-2y+3z=4Answer by ankor@dixie-net.com(16523)   (Show Source): You can put this solution on YOUR website!How do I eliminate variables using the addition method? 2x - y + z = 1 3x -3y +4z = 5 4x -2y +3z = 4 : They have made it easy, multiply the 2nd equation by -1 (change the signs) & add 2x - y + z = 1 -3x+3y -4z = -5 4x -2y +3z = 4 ------------------addition eliminates y and z +3x = 0 x = 0 : Using the original two equations without x; -y + z = 1 -3y +4z = 5 Multiply the 1st equation by -4 and add +4y -4z = -4 -3y +4z = 5 -----------------addition eliminates z y = 1 : Find z by substitution -y + z = 1 -1 + z = 1 z = 1 + 1 z = 2 : x=0, y=1, z=2 ; Check solution in original 3rd equation 4x -2y +3z = 4 4(0) - 2(1) + 3(2) = 4 0 - 2 + 6 = 4