determine which equations below when combined with the equation 3x - 4y equals two or form a system with no solutions. choose all that apply.1. 2y=1.5x-22. 2y=1.5-13. 3x+4y=24. -4y+3x=-2
Accepted Solution
A:
The equation given above is, 3x - 4y = 2 This can be expressed in slope-intercept form by transposing y to one side of the equation, y = (2 - 3x) / -4
Simplifying, y = 3x/4 - 1/2
The equations will form a system with no solution only if they have the same slope but different y-intercept.
(1) 2y = 1.5x - 2 y = 3x/4 - 1 Since this has the same slope as the given equation but different intercept then, this is one of the answers.
(2) 2y = 1.5x - 1 y = 3x/4 - 0.5
This is exactly the same as the given equation then, the equations will have infinite number of solutions.
(3) 3x + 4y = 2 4y = (2 - 3x) y = -3x/4 - 1/2
The equations do not have the same slope so, this is not one of the answers.
(4) -4y + 3x = -2 y = (-3x - 2) / -4 y = 3x/4 - 1/2 This equation is also exactly as that which is given. Hence, they will have infinite number of solutions.