, and

To solve the system, we need the inverse of A, which we write as A^-1.

Swap leading diagonal:

Change signs of the other 2 elements:

Now we find the determinant of A:

|A| = -5 - 10 = -15

So

So the solution to the system is given by:

This answer means that we have found the solution x = -2 and y = 2/5.

Is the solution correct?

We check it in the original set of equations:

Substituting x = -2 and y = 2/5, we get:

−(−2) + 5×(2/5) = 2 + 2 = 4

2×(−2) + 5×(2/5) = −4 + 2 = −2

So the solution to the original system of equations is

x = -2, y = 2/5.