If the lines 2x + y-3=0,5x+Ky-3=0 …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Aaaaa Student 4 years, 4 months ago
- 1 answers
Related Questions
Posted by Gurleen Kaur 7 months, 3 weeks ago
- 0 answers
Posted by Ananya Sv 7 months, 3 weeks ago
- 1 answers
Posted by Sethpoulou Apoulou 7 months, 3 weeks ago
- 0 answers
Posted by Sabin Sultana 7 months, 2 weeks ago
- 0 answers
Posted by Sana Dharwad 7 months, 2 weeks ago
- 0 answers
Posted by Manoj Thakur 7 months, 2 weeks ago
- 0 answers
Posted by Ashish Chaudhary 7 months, 2 weeks ago
- 1 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Gaurav Seth 4 years, 4 months ago
We know that, Three lines are said to be concurrent, if they pass through a common point which also means that the point of intersection of any two lines always lies on the third line.
Now, the three given equations of line are:
2x + y − 3 = 0 ... (1)
5x + ky − 3 = 0 ... (2)
and 3x − y − 2 = 0 ... (3)
Firstly, we will solve the equations (1) and (3) and find out the value of x and y. The corresponding value of x and y will also satisfy the equation (2) as all the given lines are concurrent.
Therefore, on adding (1) and (3), we get
2x + y − 3 + 3x − y − 2 = 0
⇒ 5x - 5 = 0
⇒ x = 1
On putting value of x in (1), we get
2(1) + y − 3 =0
⇒ y - 1 = 0
⇒ y = 1
So, the point of intersection of two lines is (1, 1).
Now, this point will also satisfy the equation (2).
Therefore, on putting (x, y) = (1, 1) in (2), we get
5(1) + k(1) − 3 = 0
⇒ k + 2 = 0
⇒ k = - 2
0Thank You