Solution:
Given, the linear pair of equations are
3x + 2ky = 2
2x + 5y + 1 = 0
We have to find the value of k.
We know that,
For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,
If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then the graph will be a pair of parallel lines.
Here, a₁ = 3, b₁ = 2k, c₁ = -2
a₂ = 2, b₂ = 5, c₂ = 1
So, a₁/a₂ = 3/2
b₁/b₂ = 2k/5
c₁/c₂ = -2/1 = -2
By using the above result,
\(\frac{3}{2}=\frac{2k}{5}\)
On cross multiplication,
3(5) = 2(2k)
15 = 4k
So, k = 15/4
Therefore, the value of k is 15/4.
✦ Try This: If the lines given by 2x + 3ky = 2 and 3x + 5y + 1 = 0 are parallel, then the value of k is
Given, the linear pair of equations are
2x + 3ky = 2
3x + 5y + 1 = 0
We are required to find the value of k.
Here, a₁ = 2, b₁ = 3k, c₁ = -2
a₂ = 3, b₂ = 5, c₂ = 1
So, a₁/a₂ = 2/3
b₁/b₂ = 3k/5
c₁/c₂ = -2/1 = -2
By using the above result,
\(\frac{2}{3}=\frac{3k}{5}\)
On cross multiplication,
2(5) = 3(3k)
10 = 9k
So, k = 10/9
Therefore, the value of k is 10/9
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 7
Summary:
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 15/4
☛ Related Questions:
The given system of equations may be written as
x + 2y + 7 = 0
2x + ky + 14 = 0
The given system of equations is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = 1, b_1 = 2, c_1 = 7`
And `a_2 = 2,b_2 = k, c_2 = 14`
The given equations will represent coincident lines if they have infinitely many solutions,
The condition for which is
`a_1/a_2 = b_1/b_2 = c_1/c_2 =. 1/2 = 2/k = 7/14 => k = 4`
Hence, the given system of equations will represent coincident lines, if k = 4
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