solve for x , y2x - 3y = -1 x+5y =7

Because the equations of the system are linear, we'll use
the matrix formed by the coefficients of the variables to calculate the determinant of
the system:

             2       
-3

det A
=

             1         5

det
A = 10+3 = 13

det A = 13 different from
zero.

Now, we'll calculate
x:

x = det x/ det
A

             -1        
-3

det x
=

             7         5

det
x = -5 - 21 = -26

x =
-26/13

x =
-2

Now, we'll calculate
y:

             2        
-1

det y
=

             1         7

det
y = 14-1

det y
=15

y = det y/ det
A

y = 15/13

y =
15/13

The solution of the
system is: {(-2 , 15/13)}