SOLUTION: PLEASE HELP!!!!!!!!!!!!!!!!!!! SOLVE FOR X 2x + y + z = 0 3x - y + z = 3 7x - 5y

SOLUTION: PLEASE HELP!!!!!!!!!!!!!!!!!!! SOLVE FOR X 2x + y + z = 0 3x - y + z = 3 7x - 5y - 3z = 15 thanks.

Question 709251: PLEASE HELP!!!!!!!!!!!!!!!!!!!
SOLVE FOR X
2x + y + z = 0
3x - y + z = 3
7x - 5y - 3z = 15
thanks.
Found 2 solutions by KMST, hheuler:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

I do not like the problem either, but no one answered yesterday, so I'll try today. (Warning: I make stupid mistakes in easy calculations, so watch for my mistakes)
Probably you want to use the elimination method, and not matrices.
You want to combine equations to get 2 combination equations with 2 variables.
(We still have a 3-variable-3-equation system, but we can set aside one of the original equations, with all 3 variables, as our third equation, and not worry about it for now).
Then, we would be able to solve the set of combination equations as a two-variable-two-equation system.

It looks like the easiest way would be to use the simpler first equation,
combining it with each of the other equations, to eliminate .
Subtracting the first equation from the second one you get

Adding times the first equation to the third one you get

Now we solve

I would subtract the new system's first equation from the other equation to get
-->
Substituting into (rather than into ) looks easy enough.
--> --> --> -->

Then, I would go back to one of the original equations and substitute and to find .
I chose as the equation that looks easiest.
--> --> -->
I verified on my own on scrap paper and it seems to work,
but remember, I warned you that I'm error prone.
Answer by hheuler(6) (Show Source): You can put this solution on YOUR website!
eq 1 2x + y + z = 0
eq 2 3x - y + z = 3
Eq 3 7x - 5y - 3z = 15
Add eq 1 and eq 2: 5x + 2z = 3 and z = 1/2[3 - 5x] eq 4
Subtract eq 1 from eq 2; x - 2y = 3 and y = 1/2[x - 3] eq 5
Substitute eq 4 and eq 5 into eq 3 giving:
7x - 5[1/2(x - 3)] - 3[1/2(3 - 5x)] = 15
Multiply both sides of this equation by 2 to eliminate the fractions and simplify the resulting equation by adding like terms. Isolate the variable x to the left side of the equation.
14x - 5x + 15 - 9 + 15x = 30
24x = 24
x = 1
From eq 4 we have z = 1/2(3 - 5(1)] = -1
From eq 5, we have y = 1/2[1 - 3] = -1
The solution is (x, y, z) = (1, -1, -1).

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