Question

I need a y and x for all of these
x+2y=8
2x- 3y=2

Answer 1

There is a few ways to solve this system of equations. What method have you been taught?

Answer 2

This is the part where a custom OS link should be posted linking the asker to a foolproof tutorial on how to solve systems of two equations using the substitution method.

Answer 3

Yes.

@pg16, look back in your class notes or text book. You must have had examples of this type of the problem. What you have almost certainly been taught is the 'method of substitution'

Take the first equation x + 2y = 8 and you can see that
x = 8 - 2y.

Substitute that into the second equation and you will have just an equation in y. Solve it.

Then find x.

Answer 4

i like elimination for these

Answer 5

susanne read fan message

Answer 6

but i do the cramer just for the practice :)

Answer 7

So here's the substitution step. The second equation is
2x - 3y = 2.

As x = 8 - 2y, we have

2(8-2y) - 3y = 2

Now solve that equation for y.

Answer 8

talk to me if you want more help here. Are you following?

Answer 9

What method have you been taught? You must have examples in the your text book and class notes. Have a read of them, copy a couple of them out. Then come back to this problem.

Answer 10

okay now I get it but can you still help me

Answer 11

He’s offline. But I’d recommend you do what he suggested; that is, go check your book and notes for a method with which to solve this system. Perhaps you were taught the substitution method. It’s not that hard.

Answer 12

hey James J can you help me

Answer 13

let's do another one first. Solve this system
x-y = 1
x+y = 3

What's the first step?

Answer 14

waiting for you

Answer 15

and I won't wait long, otherwise this whole process takes too much time.

Answer 16

change x

Answer 17

to a +

Answer 18

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

Change x? I don't know what that means.

What we want to do is eliminate one of the variables.

To do that, we need to write one variable as a function of the other. let's do that with equation (1):
x - y = 1
hence
x = 1 + y

So far so good?

Answer 19

then you plug in for the x 1+ y in the other problem

Answer 20

right

Answer 21

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

Yes, we substitute x = 1 + y into equation (2):
(1+y) + y = 3

ok? If so, now solve for y. Do that and tell me what you get.

Answer 22

1 + 2y + 3 = 6y

Answer 23

No.

(1+y) + y = 3
1 + 2y = 3 , add up the two y terms
2y = 3 -1 , subtract 1 from both sides
2y = 2 , simplify
y = 1 , divide both sides by 2

Answer 24

oh okay think I get it but can you stay here with me

Answer 25

For this system then
x-y = 1 --- (1)
x+y = 3 --- (2)

we have just found y. y = 1. What then is x?

Answer 26

From equation (1) we have that
x = y + 1.

Hence
x = what?

Answer 27

x-1=1 so we just add them right

Answer 28

so x= 2 and y = 1

Answer 29

Yes. The last step is to verify x=2, y=1 satisfies both equations
x-y = 1 --- (1)
x+y = 3 --- (2)

From (1)
x - y = 2 - 1 = 1
So equation (1) is satisfied

From (2)
x + y = 2 + 1 = 3
so (2) is satisfied.

Hence x=2, y=1 is the solution of the system of equations
x-y = 1 --- (1)
x+y = 3 --- (2)

Answer 30

Now, moving on to your system:
x + 2y = 8 -- (1)
2x- 3y = 2 -- (2)

We want to eliminate a variable. So what do you do in order to achieve that?

Answer 31

you subtract 2 from both sides

Answer 32

No! We just water through a whole example of elimination. The first we have to do is write one of the variables as a function of the other.

From equation (1),
x + 2y = 8
we can write
x = 8 - 2y

What's next?