points of intersection

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StrawberryFields

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Okay, this is totally embarassing, but I have signed up for Calc online and I can't seem to remember this stupid method from previous math classes. But this is my homework problem:

X^2 + y^2 = 25
3x + y = 15

Find the points of intersection. (there are 2)

The squares are totally messing me up..
I have gotten to
3x + 15 = sqrt(x^2 + 25)
but I don't know what to do after that
I know that it's supposed to be in general form but I can't figure it out.
 
StrawberryFields said:
Okay, this is totally embarassing, but I have signed up for Calc online and I can't seem to remember this stupid method from previous math classes. But this is my homework problem:

X^2 + y^2 = 25
3x + y = 15

Find the points of intersection. (there are 2)

The squares are totally messing me up..
I have gotten to
3x + 15 = sqrt(x^2 + 25)
but I don't know what to do after that
I know that it's supposed to be in general form but I can't figure it out.
Click to expand...

y = 15-3x

Plug that into the first eq.

x^2 + (15-3x)^2 = 25

and solve for x

You get x=4 or x=5, then plug those into the second equation and solve for the corresponding y-values.
 
I need like a good walk through.
Every step of the way
Every manipulation of the problem.
Til the end.
You don't have to give me the answer, but I really need to know exactly how to solve this

Okay so
x^2 + y^2 = 25
3x + y = 15

What are the 2 points of intersection???
 


x^2 + y^2 = 25

(The graph of this equation is a circle of radius 5 centered at the origin.)

3x + y = 15

(The graph of this equation is a line with slope -3 and y-intercept 15.)

Solve the equation of the line for y.

Substitute this result for y in the equation for the circle.

You'll get something that looks like the following.

x^2 + (mx + b)^2 = 25

(You will have actual numbers for m and b, of course.)

This is a quadratic equation.

The next step is to put this equation into general form: ax^2 + bx + c = 0.

First, expand (mx + b)^2.

If you don't know what the verb "expand" means, it means to use FOIL to multiply (mx + b) times (mx + b).

Second, simplify by combining like-terms and get everything to the left-hand side of the equation.

Reduce all coefficients by dividing both sides of the equation by their greatest common factor.

Now solve using the quadratic formula.

You will get two values for x.

To find the corresponding values for y, substitute each value for x into the slope-intercept form of the line's equation that you did above.

Write your answer as follows.

"The two points of intersection are (m, n) and (p, q)."

(You will have actual numbers for m, n, p, and q, of course.)

If you need more help, then please show your work.

MY EDIT: Added the step to reduce the coefficients
 


I had a nagging feeling that my mental arithmetic was off, so I went ahead and did the whole exercise on paper.

You won't need to use the quadratic formula.

After you get the general form ax^2 + bx + c = 0, it's very clear that the polynomial factors easily.

 
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