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
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..
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