Solve graphically

The given pair of linear equations is

2x – 3y + 13 = 0

and 3x – 2y + 12 = 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 = 2, b₁ = – 3 and c₁ = 13

and a_{2 =} 3, b₂ = – 2 and c₂ = 12

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. ( – 2,3)

Hence, the unique solution is x = – 2 and y = 3.