Question

PLease help me this is my last questions i need help with :(

The graph of a system of linear equations shows 2 lines with different slopes.


Part 1: What type of lines are they?

Part 2: Are the x and y intercepts the same or different?

Part 3: How many solutions would this system of equations have?

Answer 1

Okay im thinking that they have different slopes so they would be intercepting lines... is that correct?

Answer 2

Right - different slopes means that they have to be 2 distinct, non-parallel lines. Hence, they have a point of intersection, somewhere.

Answer 3

And ONLY 1 point.

Answer 4

They would only have 1 solution as well, and they solution would fall where they two lines intercept. Correct?

Answer 5

right.

Answer 6

Okay and now part 2 the part that is still a little confusing to me

Answer 7

Heh.... yeah, it's oddly worded. So, I'm reading it as the question is: do the 2 lines have the same y-intercepts? Do they have the same x-intercepts?

Since the lines have exactly ONE point of intersection, they COULD have the same y intercept, OR the same x-intercept. But they certainly can't have BOTH; UNLESS, both lines have x-intercept and y-intercept of (0,0). But other than THAT one case, they can't have the same x and y intercepts, if they are distinct, because that would mean TWO points of intersection, and they can't intersect at two points.

Answer 8

Do you have a graph or image or something? Maybe you are supposed to be able to tell from that.

Answer 9

Nope, it doesnt come with a graph or anything

Answer 10

OK, then like I said -

They COULD have the same x-intercepts. They COULD have the same y-intercepts. But they cant have BOTH the same, UNLESS it's the single point (0,0) (because that's the ONLY point that can be both an x intercept and a y intercept).

Answer 11

Okay what it means is when the lines pass through the Y and X axis, so would they pass through at the same number

Answer 12

Right - the x-intercept is the point of intersection with the x-axis.
y-int is the point of intersection with the y-axis.