Question 94475: Solve the system of equations. Check your solution.
-x+y-3z= -4
3x-2y+8z= 14
2x-6y+5z= -3
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! -x + y - 3z = -4
3x - 2y+ 8z = 14
2x- 6y+ 5z = -3
:
Multiply the 3rd equation by -1 and add all three equations
-x + y - 3z = -4
3x - 2y+ 8z = 14
-2x +6y- 5z = +3
-------------------Adding eliminates x and z, find y:
0x + 5y + 0z = +13
y = 13/5
y = 2.6
:
substitute 2.6 for y in the 1st equation
-x + 2.6 - 3z = -4
-x - 3z = -4 - 2.6
-x - 3z = -6.6
x + 3z = 6.6: multiplied by -1 to get rid all those negatives
:
Do the same in the 2nd equation
3x -2(2.6) + 8z = 14
3x - 5.2 + 8z = 14
3x + 8z = 14 + 5.2
3x + 8z = 19.2
:
Multiply 1st two unknown equation by 3, subtract from the 2nd two unk equaiton
3x + 9z = 19.8
3x + 8z = 19.2
-------------------subtracting eliminates x, find z
0x + 1z = +.6
z = .6
:
Use 3x - 2y + 8z = 14 to find x
3x - 2(2.6) + 8(.6) = 14
3x - 5.2 + 4.8 = 14
3x - .4 = 14
3x = 14 + .4
3x = 14.4
x = 14.4/3
x = 4.8
:
Our solution: x = 4.8; y = 2.6; z = .6
:
You should check our solutions in one of the original equations
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