Question

The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
–2 7
0 6
Line 2
x y
3 0
0 –3
A.0
B.exactly 1
C.exactly 2
D.infinitely many

The coordinates below represent two linear equations.

How many solutions does this system of equations have?

Line 1
x y
–4 3
–2 4
Line 2
x y
0 8
2 6
A.0
B.exactly 1
C.exactly 2
D.infinitely many
i rlly dont get this so could someone help? will fan and medal

Answer 1

Find the equations of both lines, then compare their slopes and y-intercepts.

I). Infinitely many solutions if both lines have the same slope and the same intercept(s).
II). No solution if they have the same slope but different intercepts.
III). One solution if they have different slopes.

Answer 2

@SolomonZelman can you help?

Answer 3

can you tell me, what is the slope of the first line?
{ knowing that it goes through points (-2,7) and (0,6) }

Answer 4

for the first one i got y=1/2x+5 but im not sure if its right

Answer 5

this is the equation of the first line, if so, then you got only the slope correctly.

Answer 6

the y-intercept is (0,6) so your first line should say not +5, but ...?

Answer 7

-5?

Answer 8

y=mx+b,
where m is the slope (which you correctly found to be 1/2)
and b is the y-intercept, which in this case is 6, since when x is 0, the y is 6. [this is given to us, by a point (0,6) ]

Answer 9

so the equation for the first line, should say?

Answer 10

y=1/2x+6?

Answer 11

yes.

Answer 12

now, the second line is going through points (3,0) and (0,-3)

Answer 13

can you find the slope?

Answer 14

y=x+-3?

Answer 15

+- ?

Answer 16

the y-intercept is when x=0... we have a point (0,-3) {this is when x=0}
so the equation of your line is: y=x..... (plus or minus 3? )

Answer 17

plus 3?

Answer 18

-3.

Answer 19

because if y-intercept is -3,
then filling in the y=mx+b we get
y=x (because we know that the slope is 1, as you have already said)
and then, y=x-3 (because y-intercept, the b, is -3)

Answer 20

okay, so your 2 equations are:

y=1/2 x+6
y= x - 3

Answer 21

can you solve for x?

Answer 22

or for y

Answer 23

I would:
~ multiply the 1st equation times -1.
~ add the (new version of the) first equation and the second equation.
~ add 9 to both sides
~ multiply the 1st equation times -1.
~ multiply both sides times 2.

this would give you the x.

Answer 24

(
first equation: y=1/2 x+6
second equation: y= x - 3
)

Answer 25

so in the first equation i multiply -1 by 1/2 or 6?

Answer 26

you multiply each thing in the first equation times -1 (for the first step)

Answer 27

~~~~~~~~~~~~~~
y times -1,
1/2 x times -1,
+6 times -1.
~~~~~~~~~~~~~~

Answer 28

im confused with solving for x or y

Answer 29

\(\large\color{black}{ b<c }\)
multiply this: y=1/2 x+6 ,times -1.
you get: -y=-1/2x-6

so now your system is:

-y= -1/2x-6
y = x - 3

Answer 30

b<c shuldn't be there, ignore that

Answer 31

so for the second equation it would be -y=-x+3?

Answer 32

you are only multiplying the first equation times -1. the second equation, leave it the way it is.

Answer 33

oh ok

Answer 34

-y = -1/2 x - 6 (<< is the result of multiplying times -1)
y = x - 3 (<< we didn't change it)


add the equations,

-y = -1/2 x - 6
y = x - 3
---------------

Answer 35

y=-1/3x-9? idk im not good with adding equations like these

Answer 36

when you add them, the Ys cancel

Answer 37

y+(-y)=?
-1/2x + x =?
-6 + (-3) = ?

Answer 38

y+(-y)=0?
-1/2x+x= -x/2?
and -6+(-3)=-9

Answer 39

yes.

Answer 40

besides that -1/2 x + x= 1/2x (not -1/2x)

Answer 41

so the addition gives us: 0=1/2 x - 9.

Answer 42

i have to go cause i have a basketball game. I'll be back tomorrow. thanks for the help though

Answer 43

okay, sure. yw

Answer 44

@sleepyjess @WHORE

Answer 45

@sleepyjess @SLUT! lol jk guys

Answer 46

Someones name is slut? LMAO

Answer 47

ikr, hilarious