Question

Find the coordinates of the points of intersection of the line y + 2x = 11 and the curve xy=12.
Help, please. Forced to do problems with little knowledge of the subject.

Answer 1

y=11-2x
put in xy=12
x(11-2x)=12
11x-2x^2=12
2x^2-11x+12=0
find x ,then corresponding values of y

Answer 2

So, I must foil then I will get the x values, right?

Answer 3

No and absolutely not. "FOIL" isn't a verb. It's not even a thing. Just solve the equation.

You can also go the other way. xy=12 ==> y = 12/x

y + 2x = 11 ==> (12/x) + 2x = 11 and solve for x.

Answer 4

I got x = 2/3 and x = 4. but I don't really know how to find the coordinates. My teacher didn't teach us this, she just told us we had to do these problems.

Answer 5

The first cannot possibly be a correct solution, Lest's see how you solved either version you have been presented.

Answer 6

I solved what I got from the other dude, but didn't make much sense.
(12/x) + 2x = 11
(12/4) + 2(4) = 11
3 + 8 = 11

Answer 7

Have you ever solved for both solutions of a quadratic equation, or just "guess and check"?

Answer 8

Yes, why do you ask?

Answer 9

I ask because that leads to both solutions, rather than just one.

Factoring...

2x^2-11x+12=0 ==> (2x - ____)(x - 4) = 0

Answer 10

2x-3, I missed type, x = 3/2

Answer 11

Good. There's a good thing to know, there. That '2' out in front suggests that denominators of solutions can be '2', but never '3'.

Okay, we have both x-coordinates. How shall we find the corresponding y-coordinates?

Answer 12

I am not sure, what should I start with? Is there a certain equation I must use?

Answer 13

Either original equation will do. Substitute the now-known values and solve.

Answer 14

Are the y values 8 and 3?
(3/2, 8)
(4, 3)

Answer 15

There you go. No more questioning.

Answer 16

Thank you so much, I was just confused about the curve and such. Didn't know if there was any additional equations or anything else that needed to be used.