4plates and 3 cups cost 20.70 dollars. 5 plates and 4 cups cost 26.40 dollars . each plates cost the same amount as the other plates , and each cup cost the same amount as the other cups. what is the cost of 1 plates ? what is the cost of 1 cup?

Here, we need to construct 2 linear equation.
Let x be the plate and y be the cup.
1) 4x + 3y = 20.70
2) 5x + 4y = 26.40

From equation 1, we solve for y.
3y = 20.70 - 4x
y = (20.70 - 4x) / 3

Substitute into equation 2.
5x + 4((20.70 - 4x) / 3) = 26.40
5x + 27.60 - 5.33x = 26.40
-0.33x = 26.40 - 27.60
-0.33x = -1.2
x = 3.64

We already get value of x. Now, calculate for value of y.
y = (20.70 - 4x) / 3
y = (20.70 - 4(3.64)) / 3
y = 2.05

The cost for 1 plate is 3.64 dollars and 1 cup is 2.05 dollars.