Question

The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
–1 6
0 4
Line 2
x y
0 7
1 5


A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many

Answer 1

can you find the slopes of the lines that the two sets of data can be modeled by?

Answer 2

The slope of Line 1 is -2 and the slope of Line 2 is -6/5

Answer 3

@SophieC12

Have another look at your calculations for line 2 (you are correct for line 1)

Answer 4

-2

Answer 5

OK good. So both lines have the same slope

What does that tell you?

Answer 6

all those pairs have the same slope....

Answer 7

(I mean the 2 lines of each pair have th esame slope as each other...)

Answer 8

Inconsistent?

Answer 9

No

If they have the same slope - do they ever touch each other (i.e. do the lines cross anywhere?)

Answer 10

I know. Inconsistent. No solution.

Answer 11

OK - I see .

yes that is correct - it means they are parallel and have no common points.

Just for completeness - the question offers the option of 'infinitely many solutions'. This would be the case if the 2 lines were actually the SAME line. You need to check whether they have the same 'y intercept' .

This is trivial in this case just look for the y value when x = 0