Question

2x-y=-2
x+2y=-1 solve

Answer 1

Well, what method for solving it have you tried?

Answer 2

the subsituten method but i forget it

Answer 3

OK. To do substitution you solve one of them for either x or y, then you replace that in the other. It is easiest to solve if you do so for a variable that does not have a coefficent. So I would sove the bottom one for x, so x = on one side and all the numbers and y on the other.

Answer 4

So, if you solve x+2y=-1 for x, what do you get?

Answer 5

could i write one as negative? then eliminate y?

Answer 6

Well, that is elimination method. There is elimination and there is substitution.

Answer 7

Elimination: Multiply one equation by a coefficent if needed so that when both equations are added, it eliminates one of the variables. Here is the simplest form example:

x+y=0
x+2y=1

In that example, if I multiply through the second by -1, I get:

x+y=0
-x-2y=-1

Then, if I add the to equations I get:
-y=-1, which means y=1 in my example. (Which is different from yours)

Answer 8

See, if I did substitution to my example it would be:
x+y=0
x+2y=1

Well, if I solve the first equation for x I get:
x+y-y=0-y
x=-y

Then, I can replace x with -y in the second:
x+2y=1
-y+2y=1
That simplifies to:
y=1

I got the same thing either way I did it. Just need to do something similar to your problem.

Answer 9

ok thanks!

Answer 10

Also, with lines you can graph them and where they intersect is the solution.

Answer 11

So, try one of those methods and tell me what you get and I can see if you did it right or not. Just be sure to use your problem and not my example, cause the numbers are different.

Answer 12

Oh, and this is an easy way to graph things to check them:
https://www.desmos.com/calculator

Answer 13

(x3,y-8)

Answer 14

(3,-8)

Answer 15

Hmm... that is not it, so do you have your calculations? Probably some sign change did not happen or some really minor thing like that. The small mistakes bite us all!

Answer 16

-x(2x-y=-2)
-2x+y=2
-x+3y=1

Answer 17

Ah, that would not eliminate anything....

2x-y=-2
x+2y=-1


Now, let me multiply through the second one by -2:

2x-y=-2
x+2y=-1

2x-y=-2
-2(x+2y=-1)

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

Now, if I add together those two equations, what do I get?

Answer 18

-5y=0

Answer 19

And what does that mean y is?

Answer 20

Goes back to the old "Anything times [ ? ] = 0" rule.

Answer 21

y=0 so i guess i cant graph this?

Answer 22

You can graph it just fine. That just means they intersect somewhere on the x axis.

OK, so plug into either of the other equations the y of 0... which basiclly means eliminate the y term thanks to the 0. Then what is x?

Answer 23

-5 is x

Answer 24

Ummm....

2x-y=-2
x+2y=-1


2x-(0)=-2
x+2(0)=-1

Solve either one.

Answer 25

or -2 is x

Answer 26

Well, 2x=-2

Answer 27

And when graphed:
https://www.desmos.com/calculator/zjvtlvv5p6

Answer 28

so (0,-2) ans (0,1)?

Answer 29

i got it thank again!

Answer 30

No, (-1,0) Remember, you found y=0 first, to the point has to end in (?,0) You are thinking (0,?) because you solved y first... but it is still y and goes in the second spot.

Both the others solve to x=-1:

2x-(0)=-2
2x=-2
2x/2=-2/2
x=-1

x+2(0)=-1
x=-1

The second had less steps, but I get the same thing.

Answer 31

If you look at the graph, you will see the lines cross at that spot too, which is a decent way to check your math. =)