Question

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

x - 3y = 3

3x - 9y = 2

Answer 1

a₁x + b₁y + c₁ = 0

a₂x + b₂x + c₂ = 0

If \(\frac{a_1}{a_2}\)= \(\frac{b_1}{b_2}\)= \(\frac{c_1}{c_2}\) infinite solution,

If  \(\frac{a_1}{a_2}\)= \(\frac{b_1}{b_2}\)≠ \(\frac{c_1}{c_2}\), no solution

If  \(\frac{a_1}{a_2}\)≠ \(\frac{b_1}{b_2}\)≠ \(\frac{c_1}{c_2}\), unique solution

x – 3y = 3

3x – 9y = 2

Thus,

\(\frac{1}{3}\) = \(\frac{1}{3}\) ≠  \(\frac{3}{2}\)

The system has no solution