Question

Use Cramer’s rule to solve for y in the following system of equations.

x + 4y – 2z = 3
x + 3y + 7z = 1
2x + 9y + z = 8

Answer 1

x + 4y – 2z = 3 , time(-1): -x-4y+2z=-3
-x- 4y+2z =-3
x + 3y + 7z = 1
ADD---------------
-y +9z = -2

x + 3y + 7z = 1, time (-2): -2x-6y-14z =-2
-2x-6y-14z =-2
2x + 9y + z = 8
ADD------------------
3y -13z =6

-y +9z = -2, time(3): -3y +27z =-6
-3y +27z =-6
3y -13z =6
ADD----------------
14z=0
z=0

Substitution z =0 find y
3y -13z =6
3y -13(0) =6
3y= 6
y =6/ 3
y=2

Substitution z =0 , y =2 find x
x + 4y – 2z = 3
x = - 4y + 2z + 3
x = - 4(2) + 2(0) + 3
x = -8 +3
x = -5

Answer 2

\[\text{LinearSolve}\left[\left( \begin{array}{ccc} 1 & 4 & -2 \\ 1 & 3 & 7 \\ 2 & 9 & 1 \end{array} \right),\left( \begin{array}{c} 3 \\ 1 \\ 8 \end{array} \right)\right]=\{-5,2,0\} \]

Answer 3

http://www.youtube.com/watch?v=taBHTo8sviM