Question

[6.01] The graph of the following system of equations is
−2x + y = 3
−4x + 2y = 6

Overlapping lines

Parallel lines

Intersecting lines

Answer 1

What is the slope of the first line?

Answer 2

3

Answer 3

The slope is -b/2a so the slope of the first line is m when you have the equation in y=mx+b form

Answer 4

Do you see that if you multiply the first equation by 2 you will get the second equation?

Answer 5

I see but how do i set up the second equation?

Answer 6

You don't. You now know that the two equations are the same and therefore the two lines are the same line.

Answer 7

so they make it Overlapping lines right??????

Answer 8

yes

Answer 9

thank you so much. can you help me one more time if you like

Answer 10

With what?

Answer 11

with this [6.03] Solve the following system.
x − y = 10
x + y = 8

(−9, 1)

(9, −1)

(9, 1)

(−1, 9)
i been taking to work it out but i think the answer is 9 -1 can you help me??

Answer 12

(9,-1) is correct

Check:

x - y = 10

9 - (-1) = 10 .. replace x with 9, y with -1

9 + 1 = 10

10 = 10 ... works

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x + y = 8

9 + (-1) = 8 .. replace x with 9, y with -1

9 - 1 = 8

8 = 8 ... works

both equations are true when x = 9 and y = -1, so (9,-1) is confirmed to be the solution

Answer 13

I got that right lol

Answer 14

nice job

Answer 15

thanks

Answer 16

no problem

Answer 17

[6.03] If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?
3x + y = 6
4x − 5y = 10

Multiply the first equation by 5.

Multiply the first equation by −5.

Multiply the first equation by −4.

Add the two equations together.

Answer 18

if you just added the equations as they are, then the y terms would add to this

y + (-5y) = y - 5y = -4y

Answer 19

but you want to make it 0y so the y terms go away when you add them

Answer 20

so be this Add the two equations together.

Answer 21

that doesn't eliminate the y variable, you have to do something before you add the equations

Answer 22

y and -5y do not add to 0y

Answer 23

Multiply them first

Answer 24

by what

Answer 25

-5y to both said

Answer 26

how do you go from y to 5y

Answer 27

idk i told you i suck at math

Answer 28

well that's why practice is important, you'll get better the more you practice

Answer 29

if we had y and -2y

we can multiply the first 'y' by 2 to get 2y giving us: 2y and -2y

they add to 2y + (-2y) = 2y - 2y = 0y

Answer 30

see how I'm doing this?

Answer 31

yes

Answer 32

so what's the final answer?

Answer 33

a

Answer 34

good

Answer 35

Thanks

Answer 36

doing that will turn y into 5y then adding the two gives: 5y + (-5y) = 0y

Answer 37

you're welcome