Graphically, the pair of equations 6x - 3y + 10 = 0 and 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
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