Which statements are true regarding the system of equations? check all that apply.

8 x + 10 y = 30. 12 x + 15 y = 60.
the lines coincide.
the lines are parallel.
the slopes are equal.
the y-intercepts are different.
the system has one solution.
the system has an infinite number of solutions.
the system has no solution.

Step-by-step explanation:

The equation of a line is

y = mx + c

where m is slope and c is the intercept

8x + 10y = 30

Refactor it to look like the equation of a line

y = -8x/10 + 30

y = -4x/5 + 30 >   (A)

For the second equation:

12x + 15y = 60

y  = -12/15x + 60/15

y = -4x/5 + 4   >   (B)

Comparing A and B

we can see that the slope of both lines are equal and that the intercepts are different

So because of the above assertions, the following are true:

- The lines are parallel

- The slopes are equal

- The y-intercepts are different

- The system has an infinite number of solutions