Question

Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions.

Answer 1

Equations are in slope-intercept form when they are given by:
y= mx + b
so named because m is the slope and b is the intercept with the y axis.
A system of two equations will be a pair of equations in this form:
y = mx + b
y = ax + c
and will have solutions at any point x that satisfies both equations.
Thus, the solutions will be found at:
mx + b = ax + c
mx - ax = c - b
(m-a)x = c - b

Clearly, in most cases we can solve this. In fact, there will only be no solution if (m-a) = 0 and c - b is not 0, because then we get 0 = c - b, which has no solution. So any system of equations:
y = mx + b
y = mx + c
b =/= c
will satisfy this. The reasoning behind this can be explained several ways, but the simplest is that the solution of a system of linear equations is the point where they intersect, and the above equations are parallel, so they will never intersect.

Answer 2

is this the answer?

Answer 3

This is a general answer to the question. You're asked to provide a system of two equations with no solution, and as I explained above the systems of equations that will have no solution will be the ones of the form:
y = mx + b
y = mx + c
Where b and c are different. So pick your favorite numbers for m, b, and c and you've got an answer. As far as explaining why there's no solution... that's why I provided the longer explanation above.