How do you solve the system using the elimination method for x-y=1 and x+y=13?

Jul 5, 2015

This system has one solution: $x = 7 , y = 6$

Explanation:

$\left\{\begin{matrix}x - y = 1 \\ x + y = 13\end{matrix}\right.$

You can see, that the coefficients of $y$ in both equations are opposite numbers (-1 and 1), so if you add the equations you will get rid of one variable:

$2 x = 14$

Now you can divide by 2 to calculate $x = 7$.

Finally when you substitute $7$ for $x$ in any of initial equations you calculate $x$ and get the full solution.