The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.
If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
Given :
[tex]y =\dfrac{2}{3}x-5[/tex]
Solution :
- An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.
- If the two lines have the same y-intercept and the slope, they are actually in the same exact line. In other words, when the two lines are the same line, then the system should have infinite solutions.
- It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.
So for example if:
Line 1 : [tex]y=\dfrac{2}{3}x-5[/tex]
than:
Line 2 : [tex]3y=2x-15[/tex]
Than this linear equations have infinite number of solutions.
For more information, refer the link given below
https://brainly.com/question/21835898
