## anonymous one year ago 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.

1. anonymous

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

2. anonymous

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

3. tkhunny

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.

4. anonymous

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.

5. tkhunny

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

6. anonymous

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

7. tkhunny

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

8. anonymous

9. tkhunny

I ask because that leads to both solutions, rather than just one. Factoring... 2x^2-11x+12=0 ==> (2x - ____)(x - 4) = 0

10. anonymous

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

11. tkhunny

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?

12. anonymous

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

13. tkhunny

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

14. anonymous

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

15. tkhunny

There you go. No more questioning.

16. anonymous

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.

17. tkhunny

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