Given:
The first equation of the system of equations is
[tex]5x+2y=-4[/tex]
To find:
The equation that gives a system with no solution.
Solution:
We have,
[tex]5x+2y=-4[/tex]
It can be written as
[tex]2y=-5x-4[/tex]
[tex]y=\dfrac{-5x-4}{2}[/tex]
[tex]y=-\dfrac{5}{2}x-2[/tex]
On comparing this equation with slope intercept form [tex]y=mx+b[/tex], we get
[tex]m=-\dfrac{5}{2},b=-2[/tex]
It means the slope of the line is [tex]-\dfrac{5}{2}[/tex] 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 [tex]-\dfrac{5}{2}[/tex] only in option D and the y-intercept is -3 which is different from -2.
The line [tex]y=-\dfrac{5}{2}x-3[/tex] is parallel to the given line and parallel lines have no solution. So, the second equation of the system of equations is [tex]y=-\dfrac{5}{2}x-3[/tex].
Therefore, the correct option is D.
