Question

Check whether the following pair of equations is consistent or not. If consistent, solve graphically:

x + 3y = 6

3y − 2x = −12 

Answer 1

x + 3y = 6   .....(i)

− 2x + 3y = −12   ....(ii)

Compare equations (i) and (ii) by a₁x + b₁y = c₁ and a₂x + b₂y = c₂

Then a₁ = 1, b₁ = 3, c₁ = 6, a₂ = −2, b₂ = 3, c₂ = −12

Then `a_1/a_2 = 1/(-2), b_1/b_2 = 3/3 = 1`

`a_1/a_2 ≠ b_1/b_2`

So, the given equations are consistent.

From equation (i)

x + 3y = 6

Put x = 0

0 + 3y = 6

y = `6/3`

y = 2

Put x = 6

6 + 3y = 6

3y = 0

y = 0

y = 0

x	0	6
y	2	0

From equation (ii)

− 2x + 3y = −12

Put x = 0

− 2 × 0 + 3y = −12

3y = −12

y = `(-12)/3`

y = −4

Put x = 6

− 2 × 6 + 3y = −12

y = 0

x	0	6
y	−4	0

Equations (i) and (ii) intersect each other at point (6, 0)

Hence, the solution of the given equations is (6, 0).