Solve this system for a and b

3a + 2b = 1
2a - 3b = -8


3(2) + 2(2) = 1(2)
2(3) - 3(2) = -8(3)

6 a + 4b = 2
6 a - 6b = -24

2b = -22

Am i doing this right so far? Thanks.

No, I am sorry to say, you are not.

If you use elimination, one line has to be multiplied by the appropriate constant so that when you add there is a variable eliminated.

You need a -6 on one of the equations so that when you add a variable disappears.

\(\displaystyle 3a+2b=1\)........multiply this row by 2

\(\displaystyle 2a-3b=-8\)..........multiply this row by -3

Then get:

\(\displaystyle 6a+4b=2\)

\(\displaystyle -6a+9b=24\)

Now, add the two equations and 'a' will be eliminated.