tips

For two linear equations $a_{1}y+a_{1}x=c_1$ and $a_{2}y+a_{2}x=c_2$ to have the same slope which we know $\frac{a_1}{a_2}=\frac{b_1}{b_2}$. However, for the lines to be different, $\frac{a_1}{a_2}\ne \frac{c_1}{c_2}$.

To simplify a fraction with linear top and bottom, use linear over linear.