Question 816184
2x + 3y = -1 
3x + 4y = -4
This problem can be solved two ways
1)  substitution
solve first equation for x
2x = -1 -3y
x = (-1 -3y) / 2
substitute for x in second equation
3*(-1 -3y)/2 +4y = -4
multiply both sides of = by 2
3*(-1 -3y) +8y = -8
-3 -9y +8y = -8
-y = -5
y = 5 
solve for x in first equation
2x +3*(5) = -1
2x = -16
x = -8
check answers in second equation
3*-8 +4*5 = -4
-24 +20 = -4
-4 = -4
therefore 
x = -8 and y = 5 is the correct solution
2) solve system of linear equations using matrices
2x + 3y = -1 
3x + 4y = -4
first write the augmented matrix using the coefficients with the right column contains the constants
| 2  3  | -1 |
| 3  4  | -4 |
The objective is to reorganize the original matrix into one that looks like
| 1  0  |  a |
| 0  1  |  b |
where a and b are the solutions to the system
multiply row 2 by -1 and add to row 1
| -1 -1  |  3 |
|  3  4  | -4 |
multiply row 1 by 3 and add to row 2
| -1 -1  |  3 |
|  0  1  |  5 |
add row 2 to row 1
| -1  0  |  8 |
|  0  1  |  5 |
multiply row 1 by -1
|  1  0  | -8 |
|  0  1  |  5 |
This gives us the solution x = -8 and y = 5
Note that this matches with our substitution solution in 1)   :-)