Question

what is the solution of the system of equations?
2x + 2y + 3z = -6
3x + 5y + 4z = 3
2x + 3y +4z = -10

Answer 1

Subtract the first equation with the last equation like this:
\[(2x+2y+3z)-(2x+3y+4z)=(-6)-(-10)\]

Answer 2

ohh ok. I can't believe I didn't notice that. I was so focused on the first and second one.

Answer 3

We're not done yet.

Answer 4

You have to multiply the first equation by 3 and then you would have to multiply the second equation by 2.
\[3(2x+2y+3z)=3(-6)\]
\[2(3x+5y+4z)=2(3)\]

Answer 5

Then you subtract to get rid of the x. Then you would have two equations with two variables: y and z.

Answer 6

ok

Answer 7

Then you can go on from there to solve those two new equations like a system.

Answer 8

ok thanks so much for explaining.

Answer 9

No worries.