Question

Consider the system of linear equations.
2y = x + 10
3y = 3x + 15

Which statements about the system are true? Check all that apply.

The system has one solution.
The system graphs parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations graph the same line.
The solution is the intersection of the 2 lines.

Answer 1

Graph the equations. Which statements are true?

Answer 2

The solution is the intersection of the 2 lines. true

Answer 3

d and e i can cross out

Answer 4

What else?

Answer 5

What is the y-intercept for the lines?

The y-intercept is when the line crosses the y-axis. It's when x = 0.

Answer 6

(0),(5)

Answer 7

Remember, you have to write points in the form of (x, y) NOT (x),(y)

Answer 8

So do the two lines have the same y-intercept?

Answer 9

right

Answer 10

no they dont

Answer 11

Don't they both cross the y-axis at the same point?

Answer 12

yes they do

Answer 13

sorry i had to look at it again

Answer 14

so you could say that they have the same y-intercept

Answer 15

ok

Answer 16

How many times do the two lines intersect?

The point at where they intersect is the solution. So does it have 0 solutions? If they're parallel lines (they have the same slope BUT not the same y-intercept), they'll have 0 solutions

Does it have an infinite number of solutions? If the lines have the same slope AND the same y-intercept, then it'll have an infinite number of solutions

Answer 17

ok

Answer 18

What are your final answers?

Answer 19

i mean a,d,f

Answer 20

Correct!

Answer 21

thank you

Answer 22

You're welcome!