Question

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

x − 2y = 0

2x + y = 0

Answer 1

x − 2y = 0    ...(i)

2x + y = 0    ...(ii)

a₁ = 1, b₁ = −2, c₁ = 0, a₂ = 2, b₂ = 1, c₂ = 0

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

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

So, equations are consistent.

From equation (i)

x − 2y = 0

Put x = 0

0 − 2y = 0

y = 0

Put x = 2

2 − 2y = 0

2 = 2y

`2/2` = y

y = 1

Put x = −2

−2 − 2y = 0

−2 = 2y

`(-2)/2` = y

y = −1

x	0	2	−2
y	0	1	−1

From equation (ii),

2x + y = 0

Put x = 0

2(0) + y = 0

y = 0

Put x = 1

2(1) + y = 0

2 + y = 0

y = –2

Put x = –1

2(–1) + y = 0

–2 + y = 0

y = 2

x	0	1	−1
y	0	−2	2

Equations (i) and (ii) intersect at the origin. 

Therefore, the solution of the system of equations is (0, 0).