How do you solve the following system?: x-7y=9 , 7y=3x+1

May 20, 2017

See a solution process below:

Explanation:

Step 1) Solve the first equation for $x$:

$x - 7 y = 9$

$x - 7 y + \textcolor{red}{7 y} = 9 + \textcolor{red}{7 y}$

$x - 0 = 9 + 7 y$

$x = 9 + 7 y$

Step 2) Substitute $9 + 7 y$ for $x$ in the second equation and solve for $y$:

$7 y = 3 x + 1$ becomes:

$7 y = 3 \left(9 + 7 y\right) + 1$

$7 y = \left(3 \cdot 9\right) + \left(3 \cdot 7 y\right) + 1$

$7 y = 27 + 21 y + 1$

$7 y = 28 + 21 y$

$7 y - \textcolor{red}{21 y} = 28 + 21 y - \textcolor{red}{21 y}$

$\left(7 - \textcolor{red}{21}\right) y = 28 + 0$

$- 14 y = 28$

$\frac{- 14 y}{\textcolor{red}{- 14}} = \frac{28}{\textcolor{red}{- 14}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 14}}} y}{\cancel{\textcolor{red}{- 14}}} = - 2$

$y = - 2$

Step 3) Substitute $- 2$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 9 + 7 y$ becomes:

$x = 9 + \left(7 \cdot - 2\right)$

$x = 9 + \left(- 14\right)$

$x = 9 - 14$

$x = - 5$

The solution is: $x = - 5$ and $y = - 2$ or $\left(- 5 , - 2\right)$