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

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using substitution method:

Step 1: Solve the second equation for y: 8x - 10 = y

Step 2: Substitute the value of y from the second equation into the first equation: 4x^2 - 5x = 8x - 10

Step 3: Simplify the equation: 4x^2 - 5x - 8x + 10 = 0 4x^2 - 13x + 10 = 0

Step 4: Factor the quadratic equation: (2x - 5)(2x - 2) = 0

Step 5: Set each factor to zero and solve for x: 2x - 5 = 0 => x = 5/2 = 2.5 2x - 2 = 0 => x = 1

Step 6: Substitute the values of x into either of the original equations to find the corresponding y-values: For x = 2.5 in the first equation: 4(2.5)^2 - 5(2.5) = y
25 - 12.5 = y
12.5 = y

For x = 1 in the first equation: 4(1)^2 - 5(1) = y
4 - 5 = y
-1 = y

Therefore, the solution to the system of equations is: x = 2.5, y = 12.5 x = 1, y = -1