# How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

Solve the first equation for x, substitute into the second equation, and get the answer of $x = 12$ and $y = 17$

#### Explanation:

To solve using substitution, we'll take one of the equations (the first one - it's a very simple one), solve for x, and then substitute it into the second one.

So let's first take $y = x + 5$ and solve for $x$:

$y = x + 5$ - subtract 5 from both sides and we get

$y - 5 = x$

And now we can substitute that into the 2nd equation:

$y = 2 x - 7$
$y = 2 \left(y - 5\right) - 7$

and let's simplify

$y = 2 y - 10 - 7$ - we can subtract $2 y$ from both sides and combine terms
$- y = - 17$
$y = 17$

We can now substitute the y value back into the given equations and find the x value:

$y = x + 5$
$17 = x + 5$
$x = 12$

$y = 2 x - 7$
$17 = 2 x - 7$
$24 = 2 x$
$x = 12$

And we're done! $x = 12$ and $y = 17$