Question

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?

Answer 1

Explanation:

Consider the following system of equations:

10 + y = 5x + x2

5x + y = 1

The first equation is an equation of a

parabola

The second equation is an equation of a

line

How many possible numbers of solutions are there to the system of equations?

0 ,1 ,2

What are the solutions to the system? (1) (-11) (56)

Answer 2

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

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)