Math problem: help!

[MD1032]

ARRRGGGHHH "Back to School" time. I have to do this review before school starts as a requirement for my Geometry (H) class. I took Alg2H last year. Anyway, I cannot figure out this problem for some reason. This wholoe "review" is a joke but the obvious on this particular problem seems to have evaded me.

"Find the value(s) of k, if any, that satisfy the given condition."

2x + ky = 6
3x - 4y = -8

Can anyone please give me some help or pointers?

[WingWizard]

use matrices;

[2 k * [x = [6
3 -4] y] -8]

Sorry, can' use brackets to enclose the whole thing; lemme know if you can't understand it

[MD1032]

OK, I can't understand it. I've never used matrices to solve a problem. Keep in mind I am a mere sophomore this year. It can't possibly be that complicated.

3 will work if y = 2 and x = 0.

Matrices are fun.

[MD1032]

Problem: I DON'T KNOW HOW TO USE MATRICES!!!

[shawshank62]

http://www.ping.be/math/matr.htm


god i dont wanna go back to school.......well i better get back to "the complete idiots guide to calculus" serisouly

[ben-the-slacker]

Edit 1: !@#%$%!#$

Messed up the equations....need to rework the problem


Edit 2: Well, my friend says it's -2.0225 and 17.365, but those numbers don't look right to me. He says he did it with some chemistry technique that took up a page of paper.

I get K = 0... think that's a valid answer?

[Redwolf]

You could try substituting for X. You'd get aeverythign down to 2 variables. IT's late and I don't want to work it out, but you should get something like a Trinomial.

[Pexster]

Try graphing --

3x - 4y = -8 is a linear equation with a slope of 3/4 and a y-intercept of 2. Graph this.

If you graph 2x + ky = 6 using a few values, say 0, 1, 2, 3, you'll see that this is also a linear equation with an x-intercept of 3. Notice that it always will intersect your 1st graph. If you then graph it using some negative integers, -1, -2, -3, you'll see that somewhere in between -2 and -3 is where the line will be parallel to your 1st equation.

So the graphs will always intersect for integer values of k. The only time they will be parallel, i.e., not intersect or not have a solution, is when the 2x + ky = 6 equation has a slope of 3/4 (same as the other equation). So . . .

2x + ky = 6

ky = 6 - 2x

y = 2x/k + 6/k

2/k = 3/4

k = -8/3

So -8/3 is the only value of k that does not work. It's not clear if they are only interested in integer values.