Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose. x - 5y + 2z = 0 x + 4y - z = 12 2x - y + 3z = 10

Answer 1

\[x - 5y + 2z = 0 \\
x + 4y - z = 12\\
2x - y + 3z = 10\]

Answer 2

x -5y +2z = 0
x +4y -z = 12
2x -y +3z = 10

I'm going to use Cramer's Rule to solve for x.
\[x_{i}=\frac{\det A_{i}}{\det A}\]

I'm using Cramer's rule because I can solve for the variable directly rather than going through extra steps. (The matrix tool on here confuses me, so you're going to have to bear with me here in this drawing.)

Answer 3

All that mess is equal to another mess.

0(4*3 - -1*-1)
+5(12*3 - -1*10)
+2(12*-1 - 4*10)
------------------------
1(4*3 - -1*-1)
+5(1*3 - -1*2)
+2(1*-1 - 4*2)

Answer 4

Which "simplifies" to
[ 5(46) + 2(-52) ] / [ (11) + 5(5) + 2(-9) ]

Answer 5

Which in turn becomes
126 / 18 = x
7 = x

Quite a lot of work to type out, but it actually goes so much more quickly writing it out than it looks.

I would choose Cramer's Rule to solve this system. Cramer's Rule is a (somewhat) quick, efficient way to directly solve for any variable in a system of equations by using matrices. By using it, I concluded that x = 7.