Question

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

x – 2y + 4 = 0, 2x – y – 4 = 0

Answer 1

x − 2y + 4 = 0    ....(i)

2x − y − 4 = 0    ....(ii)

Compare equations (i) and (ii) with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0.

Then, a₁ = 1, b₁ = −2, c₁ = 4, a₂ = 2, b₂ = −1, c₂ = −4

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

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

∴ Consistent equation.

From equation (i),

x − 2y + 4 = 0

Put x = 0 and y = 0 in equation (i),

y = 2 and x = −4

x	0	−4
y	2	0

From equation (ii)

2x − y − 4 = 0

Put x = 0 and y = 0 in equation (ii),

x	0	2
y	−4	0

Equations (i) and (ii) intersect at the point (4, 4).

Hence, the graphical solution of the equations is (4, 4).