Consider the following system of equations:

10 + y = 5x + x^2

5x + y = 1

The first equation is an equation of a parabola.

The second equation is an equation of a line.

What are the solutions to the system?

(x = - 11 and y = 56) or (x = 1 and y = - 4)

Step-by-step explanation:

The equation of the parabola is 10 + y = 5x + x² ... (1)

And 5x + y = 1 ... (2) is the straight line.

We have to find solutions to equations (1) and (2).

Now, solving equations (1) and (2) we get, 10 + (1 - 5x) = 5x + x²

⇒ 11 - 5x = 5x + x²

⇒x² + 10x - 11 = 0

⇒ (x + 11) (x - 1) = 0

Hence, x = - 11 or x = 1

Now, from equation (2),

y = 1 - 5x = 1 - 5 (-11) = 56 {When x = - 11}

And, y = 1 - 5 (1) = - 4 (When x = 1}

Therefore, the solution of the system are (x = - 11 and y = 56) or (x = 1 and y = - 4) (Answer)