How do you solve the system of equations x + 5y = 5 and x = 4 - 5y?

Feb 18, 2017

See the entire solution process below:

Explanation:

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

$x + 5 y = 5$

$x + 5 y - \textcolor{red}{5 y} = 5 - \textcolor{red}{5 y}$

$x + 0 = 5 - 5 y$

$x = 5 - 5 y$

Step 2) Substitute $5 - 5 y$ for $x$ in the second equation and solve for $y$:

$x = 4 - 5 y$ becomes:

$5 - 5 y = 4 - 5 y$

$5 - 5 y + \textcolor{red}{5 y} = 4 - 5 y + \textcolor{red}{5 y}$

$5 - 0 = 4 - 0$

$5 \ne 4$

Because $5$ does not equal $4$ there is no solution to this question or the solution is $x$ and $y$ equal the null set: $\left\{\emptyset\right\}$