4x + 5y = 10.......(1)

6x -5y = 5...........(2)

Using the elimination method, add (1) and (2):

==> 10x = 15

==> x = 15/10 = 3/2

==> **x= 3/2**

Now to calculate y, let us substitute with (2):

6x - 5y = 5

6(3/2) - 5y = 5

==> 5y = 9 - 5

==> 5y = 4

==> **y= 4/5**

4x+5y =10

6x-5y = 5

To solve for x and y.

Add the equations 5y and -5y gets eliminated. So

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

10x = 15.

x= 15/10 =1.5.

Substitute x = 1.5 in (1):

4(1.5) +5y = 10

6+5y = 10

5y = 10 -6 =4

y = 4/5 = 0.8

So x= 1.5 and y = 0.8.

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)}.**