Question

x+y=4
x-y=2
graph the linear system and determine how many solutions it has.

Answer 1

Do you have any idea how to graph those linear equations?

Answer 2

no sir.

Answer 3

Well, the easiest method of graphing linear equations is to equate it first into y.
Example. In your case, we have x+y = 4 and x-y =2
By converting this into y equation, we will have:
y = 4-x and
y = x-2
Do you know this part?

Answer 4

@MysteryOwl . can you follow?

Answer 5

i never encountered how to convert into y equation.

Answer 6

Do you know transpositions?
Let's take a look at this:
x+y = 4
What you need to do is to isolate the variable y, there, you need to subtract x from both left and right side.
So, x+y - x = 4-x
Therefore, y = 4-x
Get it now?

Answer 7

yes..

Answer 8

then what should it do after?

Answer 9

Table of values by assigning value to x to solve the value of y. We already have y = 4-x and y= x-2
So usually, we take values from -2 to +2
Therefore, using the equation y=4-x, the table will be.
x -2 -1 0 1 2
y
Can you complete it?

Answer 10

yes.. :)

Answer 11

and i'll get the ordered pairs?

Answer 12

Yes.

Answer 13

plus on the second eq. x-y=2 if i substitute -1 as x and 3 will the 3 be a -3 since y in the equation is -?

Answer 14

Yes. That is also true. But for easier calculations, we have converted the equation to y = x-2

Answer 15

can you look through my ordered pairs?

eq.1 (-2,6) (-1,5) (0,4) (1,3)
eq.2 (-1,3) (-2,4) (0,2) (1,1)

Answer 16

You have problems with the eq.2

Answer 17

:o

Answer 18

how?

Answer 19

We have x-y = 2. right?
If we let x=-2 we will have -2-y = 2
Therefore, -2+2-y = 2+2
Hence, -y = 4 so y = -4. Got it?

Answer 20

ohh,... can you give me some ordered pairs for 2?

Answer 21

That is why we converted it into y=x-2 so that you can easily compute it.
Say x= -1 y = -1-2
Therefore, y = -3

Answer 22

Can you give the other three?

Answer 23

@MysteryOwl ?

Answer 24

sorry.. got from the bathroom.. let me go through it.

Answer 25

Sure.

Answer 26

he'res the other 3 (-2,-4)(0,-2)(-2,-4)

Answer 27

is this correct now?

Answer 28

Yes. Just plot the points on the cartesian plane and graph them. To solve for it solution, just find their intersection points. You can do that algebraically or graphically.

Answer 29

thank you :D now my only problem is this one..

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

Answer 30

Just do the same thing. :)

Answer 31

convert to y equation? :)

Answer 32

Yea.

Answer 33

thanks again..