Question

Find the solution to the system of equations.

4x-3y-z=3
-3x+5y+z=9
x+2z=6

Answer 1

Have you learned "elimination?"

Answer 2

Yes, but I don't remember how to do it.

Answer 3

Multiply the first equation by 2, which means multiply every term by 2:
4x-3y-z=3 --> 8x-6y-2z=6
do that because now you have two equations, one with +2z and one with -2z

Answer 4

combine those two:
8x-6y-2z=6 (was 4x-3y-z=3)
and
x+2z=6
by adding like terms:
8x+x, -6y+0, -2z + 2z, 6 + 6
to get:
9x - 6y = 12

Answer 5

Now you need another equation with just x, y and a constant

Answer 6

4x-3y-z=3
-3x+5y+z=9
can be combined similarly, can you do it?

Answer 7

Well, it's x+2y = 12

Answer 8

so now you combine x+2y = 12 and 9x - 6y = 12 by multiplying x+2y = 12 by 3:
3x+6y = 36
and
9x - 6y = 12
add each term:
12x = 48
x=4
then solve for y by substitution in 9x - 6y = 12 and z by substitution in 4x-3y-z=3