Question

Which system (s) of equations has infinitely many solutions? Select all that apply.

a. 4x+6y=2,
b. 8x+12y=4 4x+6y=1,
c. 8x+12y=1 2x+3y=2,
d. 4x+6y=4 2x+3y=4,
e. 4x+3y=2

Answer 1

The systems of equations that have infinitely many solutions are: a. 4x+6y=2, 8x+12y=4 and c. 8x+12y=1, 2x+3y=2

Step-by-step explanation:

The systems of equations that have infinitely many solutions are:

a. 4x+6y=2, 8x+12y=4

When we multiply the first equation by 2, we get:

8x + 12y = 4

Which is the same as the second equation. Therefore, these two equations are parallel lines that overlap and have infinitely many solutions.

c. 8x+12y=1, 2x+3y=2

We can multiply the second equation by 4 to get:

8x + 12y = 8

Which is the same as the first equation. Therefore, these two equations are parallel lines that overlap and have infinitely many solutions.