4x+5y=5

8x+10y=10

To solve the system of equations:

4x + 5y = 5 ---(1)
8x + 10y = 10 ---(2)

We will use the method of substitution or elimination to find the values of x and y.

Let's start with the substitution method:

1. Solve equation (1) for x:
4x + 5y = 5
4x = 5 - 5y
x = (5 - 5y)/4

2. Substitute the value of x in equation (2):
8x + 10y = 10
8((5 - 5y)/4) + 10y = 10
Simplifying this equation gives:
2(5 - 5y) + 10y = 10
10 - 10y + 10y = 10
10 = 10

Since 10 = 10, this equation doesn't provide any useful information. Let's try the elimination method instead:

Let's multiply equation (1) by -2, which will give us:
-8x - 10y = -10 ---(3)

Now, we can add equations (2) and (3) to eliminate x:
8x + 10y = 10
-8x - 10y = -10
----------------
0 = 0

This equation tells us that 0 equals 0, which means that there are infinitely many solutions to this system of equations. In other words, any values of x and y that satisfy equation (1) will also satisfy equation (2). We cannot determine a unique solution to this system of equations.