Question

Kinda want to cry right now.. Someone PLEASE help me.. I know there is someone out there smart enough.... 25 points and Brainliest

Answer 1

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.

• 2x+3y=6

• 3y=-2x+6

• $y=-\frac{2}{3} x+2$

Change the second equation into a linear one.

• 4x+6y=12
• 6y=-4x+12
• $y=-\frac{2}{3} x+2$

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.

$y=\frac{1}{5} x+2\\y=\frac{1}{5} x+10$

These lines are parallel since they have the SAME slope but a different y-intercept. As stated above, parallel lines have no solutions.