Yea...

Question

Yea...

EndersWorld · Answer

If $$x+y=3and3x+5y=13$$ then was is $$x-y$$
I got $$-1$$ as my answer

Hero · Answer

The goal is to find a value for $x$ and a value for $y$.

EndersWorld · Answer

$$x=1$$$$y=2$$

EndersWorld · Answer

$$1-2=-1$$

Hero · Answer

And what steps did you perform to find x and y?

EndersWorld · Answer

Mental math.

Hero · Answer

No, you have to show actual steps.

Hero · Answer

Or rather, post the mental math you did in your head on paper.

EndersWorld · Answer

I know $$5*2=10$$ so I subtracted that and got $$3x=3$$ Divide by 3 and you get $$x=1$$

Hero · Answer

Or rather, electronic format in this case.

Hero · Answer

No, you have to do it deductively. That process you posted is not "deductive" or done using rules of algebra.

EndersWorld · Answer

e.e

EndersWorld · Answer

Did I not get the right answers?

Hero · Answer

Right answers, incorrect reasoning.

EndersWorld · Answer

It was mental, it doesn’t have reasoning

Hero · Answer

Okay put it this way, there are some valid ways to solve this. You can use Elimination Method or Substitution Method. You are only allowed to use one of these methods to solve it.

EndersWorld · Answer

I hate both of them

Hero · Answer

They are both essential to know.

EndersWorld · Answer

Help wizard ~-~

Hero · Answer

Let x + y = 3 represent equation (1) and 3x + 5y = 13 represent equation (2):
Then

(1) x + y = 3
(2) 3x + 5y = 13

Elimination Method is as follows:
Multiply both sides of equation (1) by 3 to get:
3x + 3y = 9
3x + 5y = 13

Subtract equation (2) from equation (1) to get:
-2y = -4

Add 4 to both sides, then 2y to both sides to get:
2y = 4

Divide both sides by 2 to get:
y = 2

EndersWorld · Answer

Ooo, then I plug in y to get x

Hero · Answer

Correct.

EndersWorld · Answer

Which would be 1

Hero · Answer

Substitution Method is as follows:
(1) x + y = 3
(2) 3x + 5y = 13

In equation (1) subtract x from both sides to get:
y = 3 - x

Substitute the expression for y in equation (2)
3x + 5(3 - x) = 13

Then solve for x:
3x + 15 - 5x = 13
         3x - 5x = 13 - 15
         (3 - 5)x = -2
               -2x = -2
                 2x = 2
                   x = 1

Hero · Answer

Plug value for x back into equation (1) to find y.

Hero · Answer

Neither method is difficult. In some cases Substitution would be simplest method. In other cases, Elimination method will be most useful.

EndersWorld · Answer

I gotcha.

EndersWorld · Answer

Moving on :)