Question

The given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.

2x + 3y = 1 

3x – y = 7

Answer 1

Let a₁x + b₁y – c = 0 ≃ 2x + 3y – 1 = 0 

a₂x + b₂y + c₂ = 0 ≃ 3x – y – 7 = 0 

Now comparing their coefficients i.e.,\(\frac{a_1}{a_2}\) and \(\frac{b_1}{b_2}\)

⇒ \(\frac{2}{3}\)≠ \(\frac{3}{-1} \)

The given lines are intersecting lines. 

2x + 3y = 1

3y = 1 – 2x 

y = \(\frac{1-2x}{3} \)

3x – y = 7

y – 3x = - 7

y = 3x - 7

The system of equations has a unique solution (2, – 1).