Solve for x and y 4x+ 5y = 10, 6x - 5y = 5.

We'll solve the system using the elimination
method.

We'll note the equations of the system
as:

4x+ 5y = 10 (1)

6x - 5y =
5 (2)

We'll add (2) to
(1):

4x+ 5y + 6x - 5y =
10+5

We'll eliminate like
terms:

10x = 15

We'll divide
by 5:

2x = 3

We'll divide by
2:

x =
3/2

We'll substitute the value of x into
(2):

6x - 5y = 5

6*3/2 - 5y =
5

9 - 5y = 5

-5y = 5 -
9

-5y = -4

We'll divide by
-5:

y =
4/5

The solution of the system
is: {(3/2 , 4/5)}.