# How do you solve x -7y=16 and -3x+6x= -3 using substitution?

May 30, 2017

The final answer is $x = - 1$ and $y = - \frac{17}{7}$

#### Explanation:

To use substitution, we must isolate $x$ on one of the sides in one of the equations. The first equation looks simple enough to manipulate and isolate $x$.

We can add $7 y$ to both sides of the first equation to get:

$x = 7 y + 16$

Now, we can turn towards the second equation. We can first simplify the left side by adding the $x$'s ( $- 3 x$ and $6 x$) to make the second equation:

$3 x = - 3$

Although we could just solve for $x$ here, we should use substitution. We can know replace $x$ with the equal value $7 y + 16$ (from the first equation) to make the second equation:

$3 \left(7 y + 16\right) = - 3$

Now we can solve the second equation from there by distributing, subtracting, and dividing:

$21 y + 48 = - 3$
$21 y = - 51$
$y = - \frac{51}{21} = - \frac{17}{7}$

To solve for $x$, we can substitute our value for $y$ into the first equation ($x = 7 y + 16$) to get:

$x = 7 \left(- \frac{17}{7}\right) + 16$
$x = - 17 + 16$
$x = - 1$.

Therefore, our final solution is $x = - 1$ and $y = - \frac{17}{7}$