Question 64991
Please answer this question for me.
If one linear equation is y=(-3)x+5, which of the following linear equations will produce a system with no solution?
A.) y=1/3+5
{{{highlight(B)}}} 6x+2y=8
C.) 4x-3y=12
D.) -3x+y=5

If you have two lines with the same slope and different y-intercepts, they are parallel and will never intersect to give you a solution.  The slope intercept form of a line is {{{highlight(y=mx+b)}}} Where m=slope and b=y-intercept.  Put the equations into slope intercept form, the one that has m=-3 and b does not = 5 is the one that will yield no solution.
Look at B.
6x+2y=8
6x-6x+2y=-6x+8
2y=-6x+8
2y/2=-6x/2+8/2
y=-3x+4
The slope m=-3 and the y-intercept b=4
This line is parallel to y=-3x+5 the lines will never intersect to give you a solution.
Happy Calculating!!!