Question

Solving a Mixed-Degree

Consider the following system of equations:
10 + y = 5x + x2
5x + y = 1
The first equation is an equation of a
The second equation is an equation of a
What are the solutions of the system?

Answer 1

The solutions are:

(1,-4), and (-11,56)

Explanation:

10 + y = 5x + x^2

5x + y = 1

Rearrange both equations to isolate y:

y = x^2 + 5x - 10

y = -5x+1

Since y=y, we set set the right sides of both equations equal to each other:

-5x+1 = x^2 + 5x - 10

Rearrange

-x^2 - 10x + 11 = 0

x^2 +10x - 11 = 0

Factor

(x+11)(x-1) = 0

x = -11 and 1

Use these two values of x to find y. We'll use the simpler equation of

y = -5x+1.

x _y

1 -4 (1,-4)

-11 56 (-11,56)

See the attached graph for proof.