Question

The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Answer 1

Line 1
x y
-2 7
0 6

Answer 2

Line 2
x y
3 0
0 -3

Answer 3

i think there's 2 solution

Answer 4

two lines will never have 2 solutions.
They can be coincident (lay on top of each other), and that would mean \(\large\color{slate}{ \infty}\) of solutions.
They can be parallel, and have no solutions because they won't intersect.
They can have different slopes, and intersect at 1 point.

Answer 5

lets find the slope of the first line, can you do that?

Answer 6

umm they tell me how to do it like this-3-(-6)
--------
-3-(-4)

Answer 7

like: \(\large\color{black}{ \frac{\LARGE y_1-y_2 }{\LARGE x_1-x_2 } }\)

Answer 8

in your case:
your points are not
\(\large\color{black}{ (x_1,y_1) }\) and \(\large\color{black}{ (x_2,y_2) }\)
but,
\(\large\color{black}{ (-2,7) }\) and \(\large\color{black}{ (0,6) }\)

Answer 9

So your slope would be equivalent to?

Answer 10

ya

Answer 11

can you calculate the slope?
I will plug in the point for you:
\(\large\color{black}{ (7-6)/(-2-0) }\)

and you give me the answer (for the slope of the first line)

Answer 12

ya and i got -1/2

Answer 13

yes, correct.

Answer 14

and -3/-3

Answer 15

3/3

Answer 16

And you are given the y-intercept to be 0,6.
So the first line would be;
\(\large\color{black}{ y=\frac{\Large 1}{\Large 2}x+6}\)

Answer 17

The slope of the second line is ? (you wrote it correctly, but didn't simplify it completely)

Answer 18

oh ya ur right it is infinity

Answer 19

3/3 is equal to what?

Answer 20

a/a=1
4/4=1
(-7)/(-7)=1

and any number divided by itself is 1.

so 3/3 = ?

Answer 21

I didn't say there are infinity of soltions here, btw, I said that it is a possible case when dealing with 2 lines

Answer 22

3/3 is equal to

Answer 23

1

Answer 24

sorry took so long

Answer 25

yes, so the slope of your second line is 1.

Answer 26

the y-intercept of your second line is -3, so, you can write the equation for a second line:

\(\large\color{black}{ y=x-3}\)

Answer 27

A solution means point(s) where the lines intersect:

line 1, \(\large\color{black}{ y=\frac{\Large 1}{\Large 2}x+6}\)

line 2, \(\large\color{black}{ y=x-3}\)

\(\large\color{black}{ \frac{\Large 1}{\Large 2}x+6=x-3}\)

Answer 28

solve for x, can you do that?

Answer 29

uymm

Answer 30

no.

Answer 31

tip to solve for x.


\(\large\color{black}{ \frac{\Large 1}{\Large 2}x+6\color{red}{-\frac{\Large 1}{\Large 2}x+3}=x-3\color{red}{-\frac{\Large 1}{\Large 2}x+3}}\)

Answer 32

simplify on both sides.

Answer 33

oh.

Answer 34

yes, so what do you get on both sides after simplfying?

Answer 35

\(\large\color{black}{ \frac{\Large 1}{\Large 2}x+6\color{red}{-\frac{\Large 1}{\Large 2}x+3}=x-3\color{red}{-\frac{\Large 1}{\Large 2}x+3}}\)

\(\large\color{black}{ \cancel{\frac{\Large 1}{\Large 2}x~}+6\color{red}{\cancel{-\frac{\Large 1}{\Large 2}x}+3}=x-3\color{red}{-\frac{\Large 1}{\Large 2}x+3}}\)

\(\large\color{black}{ 6\color{red}{+3}=x-3\color{red}{-\frac{\Large 1}{\Large 2}x+3}}\)

Answer 36

And from,
\(\large\color{black}{ 6\color{red}{+3}=x-3\color{red}{-\frac{\Large 1}{\Large 2}x+3}}\)

\(\large\color{black}{ 6\color{red}{+3}=x\cancel{-3}\color{red}{-\frac{\Large 1}{\Large 2}x\cancel{+3}}}\)

\(\large\color{black}{ 6\color{red}{+3}=x\color{red}{-\frac{\Large 1}{\Large 2}x}}\)

Answer 37

can you simplify on both sides, now?

Answer 38

9 = x -1/2

Answer 39

you got the 9 correctly

Answer 40

forgot the x

Answer 41

you can still simplify the right side, after you have:

\(\large\color{black}{ 9=x\color{red}{-\frac{\Large 1}{\Large 2}x}}\)

Answer 42

-.- aww man.....

Answer 43

tell me,
1- (1/2)

is how much?

Answer 44

hmm, les see 1/1?