Question

In which quadrant does the solution of the system fall?
x+y=4
2x-y=2

a.I
b.II
c.III
d.IV

Answer 1

do you know how to find the solution of the system?

Answer 2

would you like to use elimination or substitution methods?

Answer 3

@Quxxn

Answer 4

substitution

Answer 5

ok do you know how?

Answer 6

no /:

Answer 7

ok start by solving one of the two equations for x or for y, you choose the equation and what variable to solve for

Answer 8

the first equation looks easiest to solve for either x or y

Answer 9

is it x=4-y?

Answer 10

yep, ok now since you know x = 4 - y, look at the other equation and whereever u see an x, replace it with 4-y

Answer 11

2x-y=2
2(4-y)=2
8-2y=2
-2y=2-8
-2y=-6
y=3

Answer 12

very close but the second line you are missing a -y 2(4-y)=2 should be 2(4-y) - y=2

Answer 13

ohh hold on let me try again

Answer 14

k

Answer 15

2(4-y)-y=2
8-2y-y=2
8+ -3y=2
-3y=-6
y=2

Answer 16

yep perfect, so now you know y=2, you can replace y with 2 in either equation to solve for x, i think the first is easiest though..

Answer 17

so whats x?

Answer 18

would it be 2x-2=2? Like is that what i use to solve for x?

Answer 19

yeah that will work,

Answer 20

i would have used the first equation to get x + 2 = 4, but that will work too

Answer 21

2x-2=2
2x=2
x=2/4
x=1/2

x+2=4
x=2

??

Answer 22

yeah x = 2, the first one should look like this

2x - 2 = 2 (add 2 to both sides)
2x = 4 (added 2 to both sides)
x = 4/2
x = 2

Answer 23

oh oops lol

Answer 24

but yeah either way you get 2, so now you know x = 2 and y = 2, so you have the point (2,2), that is where both of the lines intersect, also called the solution of the system (the equations are equations of lines by the way)

Answer 25

ok so for the point (2,2), you have a positive x coordinate and a positive y coordinate, what quadrant would that be in?

Answer 26

Quadrant II right?

Answer 27

no, they are labeled starting with 1 in the upper right, and going counter clockwise, 2 in the upper left, 3 in the lower left and 4 in the lower right

Answer 28

http://www.purplemath.com/modules/plane3.htm

Answer 29

oh i forgot so then its the first quadrant?

Answer 30

yep, x values are positive and y values are positive in the first quadrant, Quadrant I

Answer 31

okay thank you!

Answer 32

yw