Answer:
a) Infinite solutions
b) No solutions
Step-by-step explanation:
First, know the following:
If the graphs intersect, there's only one solution.
If the graphs are parallel, there are no solutions.
If the graphs are the exact same line, there are infinite solutions.
For a):
Change the first equation into a linear one.
- [tex]y=-\frac{2}{3} x+2[/tex]
Change the second equation into a linear one.
- 4x+6y=12
- 6y=-4x+12
- [tex]y=-\frac{2}{3} x+2[/tex]
Boom. You have two equations which are equal. As stated above, graphs on the exact same line have infinite solutions.
For b)
They are already in linear form so hurray.
[tex]y=\frac{1}{5} x+2\\y=\frac{1}{5} x+10\\[/tex]
These lines are parallel since they have the SAME slope but a different y-intercept. As stated above, parallel lines have no solutions.
