Question

What's the solution to the system of linear equations
2x + y = 6
x - y = 6

Please show me what you did to get this answer step by step :-)

Answer 1

From the second equation:
x-y=6
add y to both sides:
x=6+y. Ok?

Answer 2

wait there's an even easier way.

Answer 3

Set y= to the rest of the stuff. And then set those equations equal to eachother. If you can remember, that, then you can solve any of these problems.

y=6-2x
y=x-6

You try setting them equal to each other and solve for x.

6-2x=x-6

Answer 4

2x + y = 6
x - y = 6
add the equations:
3x = 12
x = 4

Answer 5

x-y=6
4-y=6
y = -2

Answer 6

Okay I get that. Thank you :-)

Answer 7

\[\huge \text{Awesome!} \]

Answer 8

So then when you find your x-value, you can plug that in to EITHER equation and you'll get the same y-value. Try it for yourself to verify :-)

Answer 9

And if you get an equation that is y=2x+4 and y=2x+3, here's what happens:

2x+4=2x+3
(subtract from both sides)
0+4=3
0=-1 (zero does not equal -1, the y-values in the respective equations will never have any x-value in common). That means they're parallel since there's no intersection.

Answer 10

I meant to say (subtract 2x from both sides)

Answer 11

The answer bahrom gave me didn't add up. the second equation gave me a -6 instead of a 6.

Answer 12

6-2x = x-6

6-3x = -6

-3x = -12

x = 4

Answer 13

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

Answer 14

ah crap, I need to do this stuff on paper instead of the computer!

Answer 15

Sorry i meant 12
so x = 4

Answer 16

Okay but what is y?

Answer 17

brizy, look at my solution

Answer 18

Just plug in x to either one of the equations

Answer 19

bahrom gave me -2 as the y answer but i disagree with that.

Answer 20

Now, plugging x=4 back into the first equation:
2(4)+y = 6
y = 6-8
y=-2

Plugging x=4 into the second equation:

4-y = 6
-y = 2
y = -2

Therefore, x=4 works since y is the same value.

Answer 21

i'm not sure how u got a -6 instead of a 6. but here's how it works
x=4
y=-2
taking the same second equation you were having trouble to add up, here's what happens
(4)-(-2)=6
2 negatives is a possitive, implying that
4+2=6
6=6

Answer 22

I'm only in 8th grade math.

Answer 23

Just look over what I typed in. Does that make sense when I plugged the x-value into both equations?

Answer 24

ohhh 8th grade :D awesome!, you should play with these equations :) i hope you understand now though :)

Answer 25

Another thing you can play around is plot both of these by hand on paper. Look at the line of intersection. It's going to be where x=4 and y=-2. If you keep staring at it long enough, you'll have a better understanding of these lines.

Answer 26

Ok I did what you said brinethery. I got it now. Thank you guys :-)

Answer 27

great! That's what I wanted to hear :-)

Answer 28

anytime :)

Answer 29

Brizy, now you can help me with my linear algebra ;;-)

Answer 30

Lol yeah :-)