SOLUTION: The problem is dealing with systems of linear equations in more than two variables. I have to solve each system of equations. I have tried but can't seem to get the answer using t

Question 167863: The problem is dealing with systems of linear equations in more than two variables. I have to solve each system of equations. I have tried but can't seem to get the answer using the substitution or elimination method.
3x + 4y - z = -7
x - 5y + 2z = 19
5x + y - 2z = 5
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
3x + 4y - z = -7
x - 5y + 2z = 19
5x + y - 2z = 5
:
Add the 2nd and 3rd equations
x - 5y + 2z = 19
5x + y - 2z = 5
------------------adding eliminates z
6x - 4y = 24
:
Multiply 1st equation by 2, add to the 2nd equation
6x + 8y - 2z = -14
x - 5y + 2z = 19
------------------Adding eliminates z again
7x + 3y = 5
:
Two equation two unknowns:
Multiply the 1st two unknown eq by 3 and the 2nd eq by 4, add
18x - 12y = 72
28x + 12y = 20
-----------------
46x = 92
x =
x = 2
:
Find y using 7x + 3y = 5
7(2) + 3y = 5
14 + 3y = 5
3y = 5 - 14
3y = -9
y =
y = -3
:
Find z using the 1st equation
3x + 4y - z = -7
3(2) + 4(-3) - z = -7
6 - 12 - z = -7
-6 - z = -7
-z = -7 + 6
-z = -1
z = 1
:
Check solution on the 2nd equation:
x - 5y + 2z = 19
2 -5(-3) + 2(1) =
2 + 15 + 2 = 19; confirms our solution
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