Whether the following pair of linear equations 6x 3y 10 0 2x y 9 0 will represent

Graphically, the pair of equations

6x – 3y + 10 = 0

2x – y + 9 = 0

represents two lines which are

(A) Intersecting at exactly one point. 

(B) Intersecting at exactly two points.

(C) Coincident 

(D) parallel.

Solution:

Given, the pair of equations are

6x - 3y + 10 = 0

2x - y + 9 = 0

We have to find the graphical solution.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, then

i) the pair of linear equation is inconsistent

ii) the graph will be a pair of parallel lines and so the pair of equations will have no solution.

Here, a₁ = 6, b₁ = -3, c₁ = 10

a₂ = 2, b₂ = -1, c₂ = 9

So, a₁/a₂ = 6/2 = 3

b₁/b₂ = -3/-1 = 3

c₁/c₂ = 10/9

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Therefore, the graph of the pair of equations represents two lines which are parallel.

✦ Try This: Graphically, the pair of equations 2x - 3y + 10 = 0 and 4x - 6y + 9 = 0 represents two lines which are

Given, the pair of equations are

2x - 3y + 10 = 0

4x - 6y + 9 = 0

We have to find the graphical solution.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, then

(i) The pair of linear equations is inconsistent

(ii) The graph will be a pair of parallel lines and so the pair of equations will have no solution.

Here, a₁ = 2, b₁ = -3, c₁ = 10

a₂ = 4, b₂ = -6, c₂ = 9

So, a₁/a₂ = 2/4 = 1/2

b₁/b₂ = -3/-6 = 1/2

c₁/c₂ = 10/9

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Therefore, the graph of the pair of equations represents two lines which are parallel

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

NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 1

Graphically, the pair of equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are a. intersecting exactly at one point, b. intersecting exactly at two points, c. coincident , d. parallel

Summary:

Graphically, the pair of equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 represents two lines which are parallel

☛ Related Questions:

• 7y² - (11/3)y - (2/3). Find the zeroes of the polynomial , and verify the relation between the coeff . . . .
• Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also . . . .
• If the remainder on division of x³ + 2x² + kx +3 by x - 3 is 21, find the quotient and the value of . . . .

Graphically, the pair of equations 6x – 3y + 10 = 0, 2x – y + 9 = 0 represents two lines which are parallel.

Explanation:

The given equations are,

6x – 3y + 10 = 0

Dividing by 3

⇒ 2x – y+ `10/3` = 0  .......(i)

And 2x – y + 9 = 0  .......(ii)

Table for 2x – y + `10/3` = 0

Table for 2x – y + 9 = 0

Ex 3.2, 2 (iii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Term 1)

Last updated at July 23, 2021 by

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Ex 3.2, 2 On comparing the ratios 𝑎1/𝑎2 , 𝑏1/𝑏2 & 𝑐1/𝑐2 , find out whether the lines representing the following pair of linear equations intersect at a point, parallel or coincident (iii) 6x – 3y + 10 = 0 ; 2x – y + 9 = 0 6x – 3y + 10 = 0 2x – y + 9 = 0 6x – 3y + 10 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 6 , b1 = −3 , c1 = 10 2x – y + 9 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = −1 , c2 = 9 ∴ a1 = 6 , b1 = −3 , c1 = 10 & a2 = 2 , b2 = −1 , c2 = 9 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 6/2 𝑎1/𝑎2 = 3 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = (−3)/(−1) 𝑏1/𝑏2 = 3 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = 10/9 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 So, we have no solution Therefore, the lines represent the linear equations are parallel

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