SOLUTION: Graph both equations of eah system on the same coordinate axes. Use elimination of variables to find all pts of intersection. y = x^2 + 5x + 6 y = x + 11 Thanks

Question 187799: Graph both equations of eah system on the same coordinate axes. Use elimination of variables to find all pts of intersection.

y = x^2 + 5x + 6
y = x + 11

Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To perform elimination, simply subtract equation 2 from equation 1 to get

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

Rewrite as

Add to 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 answers are or

Now plug these values back into either equation (I'm going to use the second)

Plug in

So the first intersection is (1,12)

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

Plug in

So the second intersection is (-5,6)

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

Answer:

So the solutions are

and which gives the ordered pair (1,12)

OR

and which gives the ordered pair (-5,6)

Here's the graph to visually confirm the answer:

Graph of and
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