Question

Solve this system of equations algebraically:

y – 10 = 11x + x2

y – 12x = 30



The first solution is (–4, –18).



The second solution is (
,
).

Answer 1

(-4,-18) and (5,90)

Explanation:

I'll assume the first equation is supposed to be y – 10 = 11x + x^2

This is a parabola. The second equation is a straight line:

y – 12x = 30

We want to find the points at which these lines intersect. They will intersect for any (x,y) that

Let's rearrange the second equation to isolate y:

y – 12x = 30

y = 30 + 12x

Now we can take the this value of y and substitute it into the first equation:

y – 10 = 11x + x^2

(30 + 12x) – 10 = 11x + x^2

20 + 12x = 11x + x^2

0 = x^2 -x -20

We can factor this into (x+4)(x-5)

That means x can be either -4 or 5.

Find the value of y using these values of x in both original equations:

For x = -4

y – 10 = 11x + x^2

y = 11x + x^2 + 10

y = 11(-4)+(-4)^2 +10

y = -44 + 16 + 10

y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.

For x = 5

y – 10 = 11x + x^2

y = 11x + x^2 + 10

y = 11(5) + (5)^2 + 10

y = 55 + 25 + 10

y = 90

The second point both lines meet is (5,90).

We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.