when solving this equation, it is best to sart with a common variable.
Let's solve for Y first.
multiply each equation by a common scale.
(4)2x + 3y - z = -5
(6)3x + 2y +z = 5
(3)-3x - 4y + 2z = 8
=
8x +12y - 4z = -20
18x + 12y + 6z = 30
-9x -12y + 6z = 18
Add the bottom two
9x+ 12z = 48
Then add the top two (convert one to negative first, here I made the top negative.)
10x+ 10z = 50
With these two new equations, multiply by a common scale.
(10)9x+ 12z = 48
(-9)10x + 10z = 50
=
90x + 120z = 480
-90x -100x = -450
Add them together.
20x = 30
Divide.
X = 1.5
Substitute X into previous equation.
9(1.5)+12z = 48
multiply
13.5+12z = 48
subtract
12z = 34.5
divide
z = 2.875
finally, substitute Z and X in one of the original equations.
2(1.5) + 3y - (2.875) = -5
multiply
3 + 3y - 2.875 = -5
add 3 and that loving decimal
3y + 0.125 = -5
add that loving stuff holy forget
3y= -4.875
divide that piece of forget
y = -1.625
final answer:
X = 1.5
y = -1.625
z = 2.875
You didn't check your work.
3(1.5) + (-1.625) - 2(2.875) = -8
4.5 - 1.625 - 5.75 = -8
2.875 - 5.75 = -8
-2.875 = -8
[False statement, incorrect]2(1.5) + (-1.625) + 4(2.875) = 18
3 - 1.625 + 11.5 = 18
1.375 + 11.5 = 18
12.875 = 18
[False statement, incorrect]5(1.5) + 2(-1.625) - (2.875) = -1
7.5 - 3.25 - 2.875 = -1
4.25 - 2.872 = -1
1.378 = -1
[False statement, incorrect]The correct answers would be
x = 0
y = 2
z = 5
You have been defeated.
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