Expert: Sherman D. - 2/27/2005

Question
Hi, I'm in the matrices unit of my course however we have to solve for three variables using system of equations and matrices. Im having trouble solving this system of equations and help would be greatly appreciated. The three equations are as follows:
2x + y + 2z = 16
x + 3y - z = 37
4x - y + 3z = 4

Thank You.

Answer
2x + y + 2z = 16
x + 3y - z = 37
4x - y + 3z = 4

2x + y + 2z = 16
4x - y + 3z = 4

Multiply top by -2

-4x - 2y - 4z = -32
4x - y + 3z = 4

-2y - 4z = -32
-y + 3z = 4

-3y - z = -28
-z = 3y - 28
z = -3y + 28

x + 3y - z = 37
x + 3y - (-3y + 28) = 37
x + 3y + 3y - 28 = 37
x + 6y - 28 = 37
x + 6y = 65
x = -6y + 65

2(-6y + 65) + y + 2(-3y + 28) = 16
-12y + 130 + y - 6y + 56 = 16
-17y + 186 = 16
-17y = -170
y = 10

z = -3y + 28
z = -3(10) + 28
z = -30 + 28
z = -2

x = -6y + 65
x = -6(10) + 65
x = -60 + 65
x = 5

x = 5
y = 10
z = -2

as for doing it the Matrix way, go to www.quickmath.com and look for the work Matrices, and just go from there.

Sorry i can't be of much more help. Its been awhile since i have done Matrices.