Question

Hi can someone explain how to solve this systems of equation problem.

22x + 5y +7z=12
10x + 3y +2z=5
9x + 2y +12z=14

Answer 1

You can use matrices.

Answer 2

How do use matrices?

Answer 3

It's a bit hard to explain matrices here. Have you ever studied matrices before?

Answer 4

No

Answer 5

OK, here is another way without using matrices, it's a bit long though. Add equation (2) and equation (3), you will get \(19x+5y+14z=19\). Subtract this equation from the first equation, you will get \(3x-7z=-7\). Write the x in terms of z, and then substitute in any equation (say (3)), and write y in terms of z as well. Now you have x and y both in terms of z. Substitute these in any equation and find z. After that, get your values of x and y from the equations that you wrote in terms of z. Your answers should be \(x=0, y=1, z=1\).