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

Mar 29, 2018

$x = 3 , y = 6$

#### Explanation:

$y = x + 3 - - - \left(1\right)$

$y = 2 x - - - \left(2\right)$

substitute $y$ from $\left(2\right) \rightarrow \left(1\right)$

$\therefore 2 x = x + 3$

$\implies x = 3$

$\implies y = 2 \times 3 = 6$

$x = 3 , y = 6$

a quick mental check in $\left(1\right)$ verifies the solution

Mar 29, 2018

$x = 3 , y = 6$

#### 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:
$y = x + 3$
$y = 2 x$

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

$x + 3 = 2 x$

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

$x + 3 = 2 x \to 3 = 2 x - x \to 3 = x$

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 $y = 2 x$, then $x + 3 = 2 x$, and continue as above.

Mar 29, 2018

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 $y$ = 2
3
Which is: $y$ = 6 and $y$=6.