Question

How do you solve `y=x+3` and `y=2x` using substitution?

Answer 1

`x=3,y=6`

Explanation:

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

`y=2x---(2)`

substitute `y` from `(2) rarr(1)`

`:.2x=x+3`

`=>x=3`

`=>y=2xx3=6`

`x=3,y=6`

a quick mental check in `(1)` verifies the solution

Answer 2

`x=3, y=6`

Explanation:

Substitution in a system means that you write a variable in term of the other(s), and then replace every occurrence of that varable in the other equations.

It's easier done than said! Let's take a look at your system:
`y=x+3`
`y=2x`

Both equations give us an explicit representation of `y`. Take the first one, for example: we can see that `y` and `x+3` are the same thing. This means that, in the second equation, we can replace `y` with `x+3`, obtaining

`x+3=2x`

This is an equation involving `x` alone, and we can solve it as usual:

`x+3=2x -> 3 = 2x-x -> 3 = x`

Once we find one variable, we deduce the other using it's explicit representation: we knew that `y=x+3`, and now we know that `x=2`. Thus, `y=3+3=6`.

PS, note that this was a special case, since both equations were an explicit representation for `y`. We could have simply used transitivity to deduce that, if `y=x+3` and `y=2x`, then `x+3=2x`, and continue as above.

Answer 3

By guessing what is the value of `x` and `y`.

Explanation:

We have to find the value of `y`, which in both is the same value, by substituting the letters with guessed numbers.
We have to guess the value of `x`
Let's make the value of `x` 2.
That will become:
`y` = 2 + 3 and `y` = 22.
Simplify; `y` = 5 and `y`= 4
This can't be right because the `y`'s value is different.
Let's go up by one number: 3
That is:
`y` = 3 + 3 and `y` = 23
Which is: `y` = 6 and `y`=6.

The answer is 6.
Hope this helps!!