System of equations
A system of equations with two variables can have one solution, no solution, or infinitely many solutions.
Each equation corresponds to a line which can be expressed like:
y = mx + b
Where m is the slope and b is the y-intercept
For a system to have one solution, both lines must have different slopes, so they cross each other at one point.
If a system has no solution, both lines are parallel
If a system has infinitely many solutions, both lines are the same line (they coincide)
We have the following equation:
5x + 2y = -4
Let's solve it for y:
2y = - 5x -4
[tex]y=-\frac{5}{2}x-2[/tex]
Only one of the lines has the same slope as the given line:
[tex]y=-\frac{5}{2}x-3[/tex]
Both lines have the same slope but don't have the same y-intercept, so they are parallel.
Thus, the correct choice is D.
