Question

Find the coordinates of corner point A.−x + 2y = 2, x + y = 2, and y = 0.

Answer 1

okay so we have three lines

Answer 2

neither of them or parallel so they intersect to form a triangle

Answer 3

we are looing for the corners of this triangle

Answer 4

well the corner occurs when the two lines meet

Answer 5

when the two lines are equal to each other

Answer 6

two of the corners are easy to find because we can just plug y=0 into the equaitons

Answer 7

then useing that x that we get we can solce for the y

Answer 8

would you like me to show you an example

Answer 9

That would be great. THis has stomped me for hours.

Answer 10

okay lets look at these two lines:
x + y = 2
y = 0

Answer 11

we want to find the point where they intersect

Answer 12

well we know for that bottom line y always equals 0

Answer 13

since y equals zero we need to find the x to satisfy the top equation when y is 0

Answer 14

so just plug y=0 into the top equation

Answer 15

what does x then equal?

Answer 16

0

Answer 17

nope.
x + 0 = 2

Answer 18

what is x?

Answer 19

2

Answer 20

yes so whe y=0 and x=2 those lines meet

Answer 21

that is one of your corners

Answer 22

try and do the same thing for these two lines:
−x + 2y = 2
y = 0.

Answer 23

clearly y equals 0

Answer 24

but what does x equal?

Answer 25

-2

Answer 26

correct!

Answer 27

so the second corner is y=0 x=-2

Answer 28

now for the last one:
−x + 2y = 2
x + y = 2

Answer 29

youve probably been doing these in class, do you knwo how to solve these?

Answer 30

These are my downfall. I am not fond of finding these corner points and the problems she always gave use were so difficult.

Answer 31

well this one is actually pretty easy , once you get the hang of it

Answer 32

the first time i tried this last part i got a fraction.

Answer 33

thats not necessarily a bad thing...

Answer 34

what did you get?

Answer 35

y=4/3

Answer 36

correct!

Answer 37

and whats x?

Answer 38

really?

Answer 39

yep

Answer 40

omg i stopped there because i just knew i was wrong

Answer 41

nope not at all!

Answer 42

i can put the y into either equation, right?

Answer 43

yep

Answer 44

x=2/3

Answer 45

thats it so your third point is :
y=4/3 x=2/3

Answer 46

(2/3 , 4/3)

Answer 47

thank you so much! :)