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:
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1 Expert Answer
Ben K. answered • 05/16/16
JHU Grad specializing in Math and Science
First, put each equation into slope-intercept form. This will help because we will then have a slope for each equation. As a reminder the slope-intercept form looks like:
The coefficient 'm' is the slope of the line
The first one looks like...
subtract the 1 and the 3x from each side to get
The slope of this line is -3/4. The next equation looks like...
ky = -4x - 3 after doing similar operations.
We don't care about the -3/k term at the far right because that is the intercept. We only care about the slope term, because the problem wants us to find k such that the the lines are parallel. The thing that makes any two lines parallel is that their slopes have the same value. Thus, we want (-4/k) to be equal to (-3/4).
First, those pesky negatives cancel out.
Now you can cross-multiply to get
Now divide by 3 so that you isolate 'k'
Hey! We have now found 'k' such that the two lines are parallel.
I hope this helps! Please let me know if you have any questions.
Kiva C. Find the value of k such that the following two lines are parallel. 2x + y =5 ; x – ky = 7
4 Answers By Expert Tutors
Put 2x + y =5 into the slope intercept form y = 5 - 2x. The slope is -2. If the lines are parallel, the slopes must be equal. Put the equation x – ky = 7 into the slope intercept form y = x/k -7/k. For the slopes to be equal, 1/k = -2 or k = -1/2, so the equation becomes y = -2x +14
Bradford T. answered • 02/11/21
Retired Engineer / Upper level math instructor
Rewrite both equations in y = mx+b form
y = -2x +5
ky = x-7 --> y = (x -7)/k --> y = x/k - 7/k
To make the lines parallel, both lines need to have the same slope which is -2.
1/k = -2 --> k = -1/2
Niko M. answered • 02/11/21
Spreading mathematics throughout the land
The slopes of both lines must be equal in order to be parallel.
First line can be y = -2x + 5, so slope is -2
Second line can be y = (1/k)x - 7/k, so slope is 1/k
Since slopes must be equal, then -2 = 1/k , or -2k = 1, or k = -1/2
Jarom L. answered • 02/11/21
Passionate Tutor Specializing in Middle School through College Math