Four oranges and five apples cost $2. three oranges and four apples cost $1.56. find the cost of an orange and the cost of an apple.

4o + 5a = 2
3o + 4a = 1.56

You can solve by elimination or substitution, I prefer elimination.

On a problem like this you are going to have to multiply both equations to either eliminate the x terms or y terms.  I'm going to get rid of the x's just because that's what I usually do.

So

-3(4o + 5a = 2)
4(3o + 4a = 1.56)

Now you have:

-12o -15a = -6
12 o + 16 a = 6.24

Add straight down and you are left with 

1a = .24

So apples cost 0.24

Now substitute this into one of the original equations and solve for the cost of the oranges. I'll use the first equation

4o + 5(.24) = 2

4o + 1.2 = 2

4o = .8

o = .2

So oranges cost 0.20