Question 55014
if we put this into a matrix, we get:

[2   -3     4]
[5    4    33]

I'm going to multiply the top line by 5 and the bottom line by -2

[10  -15   20]
[-10  -8  -66]

I'll at the top and bottom lines together and make the sum be the new bottom line

[10   -15   20]
[ 0   -23  -46]

ok...I'm going to get back to some smaller numbers. I'll divide the top line by 5 and the bottom line by -23

[2   -3    4]
[0    1    2]

Now, I'll multipy the bottom line by 3

[2   -3   4]
[0    3   6]

Here, I'll add the two lines together and put them in the top line

[2   0  10]
[0   3   6]

Almost there. I'm going to get to the identity matrix by dividing the top line by 2 and the bottom line by 3

[1   0  5]
[0   1  2]

We get  x = 5 and y = 2!

CHECK:

We'll plug our answers into the original equation to check our work

2x-3y=4
2(5) - 3(2) = 4
10 - 6 = 4
4 =4   Check!

5x+4y = 33
5(5) + 4(2) = 33
25 + 5 = 33
33 = 33 Check!