explain how to recognize when a system of equations has no solution.
i will give !

There are two ways to solve a system of linear equations (equations representing a line) of two or more equations and find if there is a solution (or solutions) that satisfies all the equations in the system at the same time or if there is not solution.

1. Graphically, plotting the graphs of the lines and determining if they intersect and in which point.

2. Algebraically, combining the equations to delete each unknown except one, and then clear it.

In this context, a system of linear equations has no solution when the two lines are parallel and distinct, that is, they do not intersect or there is no intersection point.

Now, when two lines are parallel they have the same slope. We will be able to recognize it if we write the equation in the slope-intersect form:

Where is the slope and the intersection point.

Compare the slopes and y-intercepts of the two equations by putting them in slope-intercept form. If the slopes are equal, but the y-intercepts are different, then the lines are parallel and have no solution because they do not intersect at any point.