Question

Which systems of equations have no solutions? (Check all that apply.)

A. x – y = 1, –3x + 3y = 3

B. 2y = 3 – 4x, x + y = 0

C. 12x + 2 = 4y – 10, 2x + y = –11

D. –3x – y = 5, 15x = 10 – 5y

E. x + y = 1, –4x + 2y = 7

Answer 1

The systems of equations A and E have no solutions.

Step-by-step explanation:

The systems of equations that have no solutions are:

• A. x – y = 1, –3x + 3y = 3
• E. x + y = 1, –4x + 2y = 7

In order for a system of equations to have no solutions, the lines represented by the equations must be parallel and never intersect. In these two systems, the lines have different slopes and different y-intercepts, so they are not parallel and will intersect at a unique point, meaning they have solutions.