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

Solution:

From the above question, we have the equation as,

3x + y + 4 = 0-----------------(1)

6x - 2y + 4 = 0----------------(2)

Comparing with the general form of straight line ax + by + c = 0, we get,

a₁ = 3, b₁ = l c₁ = 4

a₂ = 6, b₂ = -2 c₂ = 4

a₁/a₂ = 1/2;

b₁/b₂ = 1/-2;

c₁/c₂ = 1.

a₁/a₂ ≠ b₁/b₂.

Hence, the given pair of linear equations are intersecting at one point and these lines have a unique solution.

Therefore, the given pairs of linear equations are consistent.

Let us graphically illustrate this.

We have, 3x + y + 4 = 0.

y = -4 - 3x.

x	0	-1	-2
y	-4	-1	2

6x - 2y + 4 = 0

2y = 6x + 4

y = 3x + 2

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).

Therefore, the above pairs are consistent.

✦ Try This: By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them. 3x + y + 6 = 0, 6x - 2y + 6 = 0

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

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NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 11 (i)

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

Summary:

By the graphical method, the following pairs of equations 3x + y + 4 = 0 and 6x - 2y + 4 = 0 are consistent.

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