Question 1106903: determine the value of k for which the system of linear equations has infinitely many solutions. then find all the solutions corresponding to this value of k
3x+4y=12
x+ky=4
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
3x+4y=12
x+ky=4
In order for the two equations to have infinitely many solutions, the equations must be equivalent. Multiply the second equation by 3; now the two equations are
3x+4y=12
3x+3ky=12
For the equations to be equivalent, we must have equal coefficients for y: 3k=4; so k = 4/3.
I will guess that by "listing all solutions" you are looking for parametric equations. To get them, solve the equation for y and then use x as the parameter:
3x+4y = 12
4y = -3x+12
y = (-3/4)x+3
The parametric equations representing all solutions are
x = t
y = (-3/4)t+3
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