Question 209868: how do I eliminate variables using the addition method?
2x-y+z=1
3x-3y+4z=5
4x-2y+3z=4
Answer by ankor@dixie-net.com(22740)   (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
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