SOLUTION: What is the solution to the system of equations x^2 - x + 6 = y and 2x + 2y = 36? Answer 187449 by richwmiller(1774) About Me on 2010-01-09 17:12:13: You can put this solution

Question 255158: What is the solution to the system of equations x^2 - x + 6 = y and 2x + 2y = 36?
Answer 187449 by richwmiller(1774) About Me on 2010-01-09 17:12:13:
You can put this solution on YOUR website!
x = -2 sqrt(3), y = 2 (9+sqrt(3)) x=-3.4641, y=21.4641
x = 2 sqrt(3), y = -2 (sqrt(3)-9) x=3.4641, y=14.5359
It is a line crossing a parabola.
Please explain this in detail thank you so much
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Rearrange the equation.

Move onto the second equation

Plug in

Distribute

Get every term to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the solutions in terms of 'x' are or

which approximate to or

Now let's find the corresponding solution for y when

Start with the given equation.

Plug in

Square to get

Combine like terms.

So when , which approximates to

Now let's find the corresponding solution for y when

Start with the given equation.

Plug in

Square to get

Combine like terms.

So when , which approximates to
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