Question

2x + 3y = -17 is one equation in a coincidental system of two linear equations. The other equation is ( )y =( )x – 102. Can you please help me find the other equation?

Answer 1

You can get another coincidental equation just by multiplying the first equation by any number.
\(\begin{array}{ccccc}y&=&mx&+&c\\2y&=&2mx&+&2c\end{array}~~~\bf{\rightarrow}
\sf~~~both~are~coincident\)
In this case you are given with another equation which is formed by multiplying the first equation by a certain amount. Since both of the equations has one known value which is the intercept(c), you can get the amount from which the first one was multiplied from \(\Large\frac{c_2}{c_1}\). So to get the second equation, multiply the first by \(\Large\frac{c_2}{c_1}\).

\(\begin{array}{ccccc}\qquad~y_1&=&m_1x&+&c_1\\\\\qquad\Large\frac{c_2}{c_1}\normalsize\times~y_1&=&\Large\frac{c_2}{c_1}\normalsize\times~m_1x&+&\Large\frac{c_2}{c_1}\normalsize\times~c_1\\\\\qquad\Large\frac{c_2}{c_1}\normalsize~y_1&=&\Large\frac{c_2}{c_1}\normalsize~m_1&+&c_2\end{array}\)

Remember not to neglect the coefficients of x and y in first equation.