4x2-5x=y 8x-10=y

To solve the system of equations, we can set the two equations equal to each other since they both equal y.

4x^2 - 5x = 8x - 10

Rearrange the equation into quadratic form:

4x^2 - 13x + 10 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use factoring:

(2x - 5)(2x - 2) = 0

Setting each factor equal to 0:

2x - 5 = 0 or 2x - 2 = 0

Solving for x in each equation:

2x = 5 or 2x = 2

x = 5/2 or x = 1

Now that we have the values of x, we can substitute them back into one of the original equations to find the corresponding values of y.

For x = 5/2:

4(5/2)^2 - 5(5/2) = y 50/4 - 25/2 = y 25/4 - 25/2 = y -25/4 = y

So one solution is (x, y) = (5/2, -25/4).

For x = 1:

4(1)^2 - 5(1) = y 4 - 5 = y -1 = y

So another solution is (x, y) = (1, -1).

Therefore, the system of equations has two solutions: (5/2, -25/4) and (1, -1).