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

Algebra.Com
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

RELATED QUESTIONS

how to eliminate variables by using the addition method?. 3x-4y+4z=7 x-y-2z=2... (answered by stanbon)
solve by addition method. I am really good at adding 2 equations usually but 3 is hectic, (answered by ikleyn,josgarithmetic,MathTherapy)
2x + 3z = 4 3y + 2z = 5 3x + 4y = −16 (x, y, z) = 2x +... (answered by Alan3354)
i need help solving this problem :/ solve by using the addition method: 5x + 3y - z = 5 (answered by ankor@dixie-net.com)
2x+3y-z=4 3x+2y+2z=6 4x-y+3z=5 solve in three... (answered by josmiceli)
Solve by sustituion and the addition method: x+y-z=8 2x+y+z=1 x+2y+3z=-5 It looks (answered by )
need help solving linear equation in three variables using the elimination method.... (answered by ankor@dixie-net.com)
How do I solve:-5x+y-4z=60 How do I solve: -2x+5y+3z=-25 in variables... (answered by Alan3354)
Solve using addition method x+3y+z=6 3x+y-z=-2... (answered by Alan3354)