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:
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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
x | 0 | `-5/3` |
y | `10/3` | 0 |
Table for 2x – y + 9 = 0
x | 0 | `-9/2` |
y | 9 | 0 |
Hence, the pair of equations represents two parallel lines.
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