Question

Solve them graphically.

x + 2y = 6 

2x + 4y = 12

Answer 1

From the given pair of equations,

a₁/a₂ = 1/2 ;

b₁/b₂ = 2/4 = 1/2 ;

 c₁/c₂ = 6/12 = 1/2

∴ a₁/a₂ = b₁/b₂ = c₁/c₂

∴ The lines are dependent and have infinitely many solutions.

x + 2y = 6

2y = 6 – x 

y = \(\frac{6-x}{2}\)

2x + 4y = 12

4y = 12 – 2x (or) 4y = 2(6 – x)

y = \(\frac{12-2x}{4 }\) or y = \(\frac{6-x}{2}\)