Question

Determine which equations below, when combined with the equation 3x-4y=2, will form a system with no solutions. Choose all that apply.
A) 2y = 1.5x - 2
B) 2y = 1.5x - 1
C) 3x + 4y = 2
D) -4y + 3x = -2

Answer 1

Two equations will not have solution if they are parallel and have different y-intercepts. Parallel lines have the same slope. In a slope-intercept form, the equation of the line can be expressed as,       
 
        y = mx + b 

where m is slope and b is the y-intercept.

Given: 3x - 4y = 2
Slope-intercept: y = 3x/4 - 1/2

A. 2y = 1.5x - 2
Slope-intercept: y = 3x/4 - 1

B. 2y = 1.5x - 1
Slope-intercept:  y = 3x/4 - 1/2

C. 3x + 4y = 2
Slope-intercept:  y = -3x/4 + 1/2

D. -4y + 3x = -2
Slope-intercept: y = 3x/4 + 1/2

Hence, the answers to this item are A and D.