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=(-5x-4)/(2)`

`y=-(5)/(2)x-2`

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

`m=-(5)/(2),b=-2`

It means the slope of the line is
`-(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
`-(5)/(2)` only in option D and the y-intercept is -3 which is different from -2.

The line
`y=-(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=-(5)/(2)x-3`.

Therefore, the correct option is D.