Question

Write the condition for a unique solution.

Answer 1

Describe the condition for a unique solution:

Consider the following equations:

$\begin{array}{rcl}{a}_{1}x+b_{1}y+c_1& =& 0\\ a_{2}x+b_{2}y+c_2& =& 0\end{array}$

These equations have a unique solution if $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$.

If and only if the specified linear equations in two variables meet at a single point, the solution will be unique for both equations.

Hence, the equations $\begin{array}{rcl}{a}_{1}x+b_{1}y+c_1& =& 0,a_{2}x+b_{2}y+c_2=0\end{array}$ have a unique solution if $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$.