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

@Astrophysics ?

Answer 2

So first find the slope for each line or rise over run

Answer 3

okay one second

Answer 4

would it be D?

Answer 5

What are the slopes? If they both have the same slope, then yes it is D or infinite solutions

Answer 6

I got -2/1 for both slopes :)

Answer 7

Yup I got the same as well. So on a graph it would just look like 1 slope as they are on top of each other

Answer 8

Thus when we are looking for solutions which are intersections, we can say infinite solutions because the slopes will intersect continuous on forever

Answer 9

thanks :) I do have a question

Answer 10

Sure

Answer 11

how would I know if the answer was 1, 2, or 0?

Answer 12

They would have 1 solution if they had different slopes because eventually the different slopes would intersect at 1 point

Answer 13

Wait!

Answer 14

okay

Answer 15

We are not done! So after we have both slopes we use the point slope formula https://www.mathsisfun.com/algebra/line-equation-point-slope.html

Answer 16

So with the same slopes we use the point slope formula