Question

The coordinates below represent two linear equations.
How many solutions does this system of equations have?
Line 1
x y
–4 5
0 2
Line 2
x y
0 5
4 2

A. 0
B. exactly 1
C. exactly 2
D. infinitely many

Answer 1

the slope of each is

line 1 --- m = -3/4
line 2 --- m = -3/4

the two are parallel from that

Answer 2

but in the table for each , when x is zero, they have different y values,

2 parallel lines, they have no solutions

Answer 3

so a

Answer 4

y = -3/4 x + 2
y = -3/4 x + 5

Answer 5

how about these
Line 1
x y
–4 8
4 6

Line 2
x y
–1 1
3 5

Answer 6

@DanJS

Answer 7

can you put the equation for each of them together ?

Answer 8

what do u mean

Answer 9

you get 2 points on each line, what is the equation of each line?

Answer 10

I didnt understand this lesson at all

Answer 11

i think construction the equation for a line was before the lesson about determining how many solutions a system of 2 equations has

Answer 12

not for my k12 online school

Answer 13

given 2 points, calculate the slope, and use

y - y1 = m*(x - x1) to make the line, (x1,y1) is any point you know on the line

Answer 14

im so confused but ill try

Answer 15

line one the slope is - 0.25 line 2 the slope is 1

Answer 16

@DanJS

Answer 17

k...

Answer 18

Line 1
slope = (6-8)/(4-(-4)) = -2/8 = -1/4

Line 2
Slope= (5-1) / (3 - (-1)) = 4/4 = 1

Answer 19

I think its b but im not quite sure

Answer 20

good, then use the slope and one of the points on the line, and make the point slope equation

Line 1
y - y1 = m*( x- x1)

y - 6 = (-1/4)*(x-4)

Answer 21

Line 2

y - 5 = 1 *(x-3)

Answer 22

what do we have to find again>?

Answer 23

oh yeah , how many solutions for the system

Answer 24

so b right???

Answer 25

a simple thing to notice, is the two lines have different slopes

they must intersect then somewhere

that is a solution

Answer 26

what is b)

Answer 27

so they would have one solution b

Answer 28

yeah , 2 lines with different slopes are not parallel, so they will cross eventually somewhere

Answer 29

the same answers as the last question sorry

Answer 30

2 lines will either

--intersect at some point (x,y) and have one solution to the system

--Be parallel and never intersect, no solutions for this case

-- be the same line , one as just a multiple of the other, infinite solutions in this case