Question

By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

3x + y + 4 = 0, 6x – 2y + 4 = 0

Answer 1

Given pair of equations are

3x + y + 4 = 0   ......(i)

And 6x – 2y + 4 = 0  .......(ii)

On comparing with ax + by + c = 0, we get

a₁ = 3, b₁ = 1 and c₁ = 4   ......[From, (i)]

a₂ = 6, b₂ = –2 and c₂ = 4   ......[From (ii)]

Here, `a_1/a_2 = 3/6 = 1/2`;

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

And `c_1/c_2 = 4/4 = 1/1`

∵ `a_1/a_2 ≠ b_1/b_2`

So, the given pair of linear equations are intersecting at one point,

Therefore these lines have unique solution.

Hence, given pair of linear equations are consistent.

We have, 3x + y + 4 = 0

⇒ y = – 4 – 3x

We have, 3x + y + 4 = 0

⇒ y =  – 4 – 3x

x	0	– 1	– 2
y	– 4	– 1	2

And 6x – 2y + 4 = 0

⇒ 2y = 6x + 4

⇒ y = 3x + 2

x	– 1	0	1
y	– 1	2	5

Plotting the points B(0, – 4) and A(– 2, 2), we get the straight line AB,

Plotting the points Q(0, 2) and P(1, 5), we get the straight line PQ.

The lines AB and PQ intersect at C(– 1, – 1).