Solve graphically the following system of linear equations if it has unique solution:

3x — 5y = —1

2x — y = —3

The given pair of linear equations is

3x – 5y = – 1 or 3x – 5y + 1 = 0

and 2x – y = – 3 or 2x – y + 3 = 0

On comparing the given equations with standard form of pair of linear equations i.e. a₁ x + b₁y + c₁ = 0 and a₂ x + b₂y + c₂ = 0, we get

a₁ = 3, b₁ = – 5 and c₁ = 1

and a_{2 =} 2, b₂ = – 1 and c₂ = 3

The lines representing the given pair of linear equations will intersect at a point.

Now, table for or

Now, table for or

Here, the lines intersecting at point B i.e. ( – 2, – 1)

Hence, the unique solution is x = – 2 and y = – 1.