Question

The first equation in a system is 5x + 2y = –4. Which equation gives a system with no solution? A. y = 2x + 6 B. y = 1/4x – 2 C. y = 2x + 7 D. y = –5/2x – 3

Answer 1

Given:

The first equation of the system of equations is

$5x+2y=-4$

To find:

The equation that gives a system with no solution.

Solution:

We have,

$5x+2y=-4$

It can be written as

$2y=-5x-4$

$y=\dfrac{-5x-4}{2}$

$y=-\dfrac{5}{2}x-2$

On comparing this equation with slope intercept form $y=mx+b$, we get

$m=-\dfrac{5}{2},b=-2$

It means the slope of the line is $-\dfrac{5}{2}$ and the y-intercept is -2.

Slope of parallel lines are same but the y-intercepts are different.

From the given options, the slope of the line is $-\dfrac{5}{2}$ only in option D and the y-intercept is -3 which is different from -2.

The line $y=-\dfrac{5}{2}x-3$ is parallel to the given line and parallel lines have no solution. So, the second equation of the system of equations is $y=-\dfrac{5}{2}x-3$.

Therefore, the correct option is D.