Question

The first equation in a system is 5x+2y=-4Which equation gives a system with no solution

Answer 1

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

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

Only one of the lines has the same slope as the given line:

$y=-\frac{5}{2}x-3$

Both lines have the same slope but don't have the same y-intercept, so they are parallel.

Thus, the correct choice is D.