# Solving for an unknown in a system of equations

• Jun 19th 2012, 04:38 PM
astuart
Solving for an unknown in a system of equations
I'm not sure whether there's a limit on the amount of questions we can post, especially when they're closely related, but I'm finding I'm struggling with math after 6 years out of school. Chem, funnily enough seems to be a hell of a lot easier :/.

Anyway, the questions is as follow..

"Determine the value of k for which the system of linear equations has infinitely many solutions. Then find all solutions corresponding to this value of k.

3x + 4y = 12
x + ky = 4

Seeing as the two lines are the same line (infinite solutions), the equations should basically be equal.

In y-intercept form, the first equation becomes y = -(3/4)x + 3.
If x = 0, then y should equal 3, right?

Assuming that the line is the same, then

"x + ky = 4" becomes 3 = -(0/k) + (4/k).
3 = (4/k)
12 = k.

Now, when I use this value, the equations don't work out to be parallel, so I'm going wrong somewhere, but I'm just not sure where..
• Jun 19th 2012, 05:04 PM
skeeter
Re: Solving for an unknown in a system of equations
both lines are the same if all the coefficients of one equation are multiples of the other

3x + 4y = 12

x + ky = 4

the first equation's coefficients are 3 times the second ... or the second equation's coefficients are 1/3 the first.

k = 4/3
• Jun 19th 2012, 05:11 PM
astuart
Re: Solving for an unknown in a system of equations
Thanks!

I was miles off :(.