Question

If ratio of coefficients of x is not equal to the ratio of coefficients of y in a given pair of linear equations in two variables then, what will be the type of graph?
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Answer 1

Answer:

the graph is consistent and independent.

Step-by-step explanation:

Given :

The ratio of coefficients of x is not equal to the ratio of coefficients of y in a given pair of linear equations in two variables

To find :

the type of graph  

Solution :

Let the pair of linear equations in two variables be

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0

where

a₁ and a₂ are coefficients of x

b₁ and b₂ are coefficient of y

As given,

$\sf \dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$

It means, the given pair of linear equations has a unique solution.

i.e., The two lines of two equations intersect at a single point.

Since it has a solution, the graph is consistent.

If a consistent system has exactly one solution, it is independent.

So, it is also independent.

Therefore, If ratio of coefficients of x is not equal to the ratio of coefficients of y in a given pair of linear equations in two variables then the graph is consistent and independent.

For example,

Consider two equations satisfying the given condition,

2x + 3y - 12 = 0

x + 2y - 8 = 0

ratio of coefficients of x = 2/1 = 1

ratio of coefficients of y = 3/2

1 ≠ 3/2

Find the solutions for first equation 2x + 3y - 12 = 0  ;

• Put x = 0,

2(0) + 3y - 12 = 0

 3y = 12

  y = 12/3

  y = 4

(0,4)

• Put y = 0,

2x + 3(0) - 12 = 0

2x = 12

  x = 12/2

  x = 6

(6,0)

• Put x = 4,

2(3) + 3y - 12 = 0

6 + 3y - 12 = 0

3y - 6 = 0

3y = 6

 y = 2

(3,2)

Plot these points and join them.

Find the solutions for the second equation x + 2y - 8 = 0 ,;

• Put x = 0,

0 + 2y - 8 = 0

2y = 8

 y = 8/2

 y = 4

(0,4)

• Put y = 0,

x + 2(0) - 8 = 0

 x - 8 = 0

 x = 8

(8,0)

• Put x = 2,

2 + 2y - 8 = 0

2y - 6 = 0

 2y = 6

  y = 6/2

 y = 3

(2,3)

Plot these points and join them.

The two lines intersect at a single point which means the pair of linear equations in two variables has a unique solution.

A consistent system of equations has at least one solution. Since 2x + 3y - 12 = 0  and x + 2y - 8 = 0  has a solution. It is said to be consistent.  

Answer 2

Answer:

This is your right answer.

Hope it will help you..