Question

How many solutions can a system of linear equations have?

Answer 1

Hint:
In the above problem, we were asked how many solutions a linear equation can have. There are three types of solutions that a linear equation has. We will see what those are in detail. The basic form of a linear equation is $Ax+By+c=0$. So, let’s see how we can solve this problem.

Complete step by step solution:
A linear equation has 3 types of solutions. They are:
1) One solution.
2) Infinitely many solutions.
3) No solutions at all.
When there is one solution it means that there is only a single intersection between two lines.
When there are infinitely many solutions it means that both the equations are referring to the same line.
When there is no solution it means that the two lines are parallel to each other and they never intersect each other.

Note:
An easy way to check if the given equation has no solution is that when the slope for both the lines is the same but they have different y-intercepts. In the equation $y=mx+c$, m is the slope. Also, the concept of x-axis and y-axis can be better understood when represented on a graph.