SOLUTION: Can you help me solve this system algabraically and support the solutions graphically? y+x^2 9x-y=20 (ordered pairs)

Question 151297: Can you help me solve this system algabraically and support the solutions graphically?
y+x^2
9x-y=20
(ordered pairs)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
What is equal to? This is not an equation.

Did you mean to say ??

Start with the second equation.

Plug in

Subtract 20 from both sides.

Rearrange the terms.

Notice we have a quadratic equation 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

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the x answers are or

Go back to the first equation

Plug in

Square 4 to get 16.

So the first set of answers is and which form the ordered pair (4,16)

----------------

Go back to the first equation

Plug in

Square 5 to get 25.

So the second set of answers is and which form the ordered pair (5,25)

==========================================

Answer:

So the ordered pair solutions are (4,16) and (5,25)

Notice that if we graph the two equations, we get

Graph of (red) and (green).

It's hard to see, but with the help of a graphing calculator, we can see that the graphs intersect at the points (4,16) and (5,25). So this verifies our answer.

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