Question

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. $3x-5y=20$ and $6x-10y=40$.

Answer 1

Solution.

The given equations are $3x-5y=20$ and $6x-10y=40$.

Here,

$$\begin{gathered} \frac{a_1}{a_2}=\frac{3}{6} \\ =\frac{1}{2} \\ \frac{b_1}{b_2}=\frac{3}{6} \\ =\frac{1}{2} \\ \frac{c_1}{c_2}=\frac{3}{6} \\ =\frac{1}{2} \\ \therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2} \end{gathered}$$

Since the given sets of lines are overlapping each other there will be infinite number of solutions for this pair of equation.

Hence, the given equations have infinite number of solutions.