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The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if
- a)k = 6
- b)k ≠ 6
- c)k = 0
- d)k ≠ 0
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 inters...
Since the pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other;
∴ (a1/a2) ≠ (b1/b2)
⇒ k/2 ≠ 3/1
⇒ k ≠ 6
∴ (a1/a2) ≠ (b1/b2)
⇒ k/2 ≠ 3/1
⇒ k ≠ 6
Most Upvoted Answer
The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 inters...
Explanation:
Intersection of Linear Equations:
When two linear equations intersect each other, it means they have a common solution, which is the point where the two lines representing the equations meet on the coordinate plane.
Given Equations:
The pair of linear equations is kx + 3y + 1 = 0 and 2x + y + 3 = 0.
Conditions for Intersection:
For the two equations to intersect each other, they must have a unique solution, which means they should not be parallel lines. The condition for parallel lines is that the coefficients of x and y in the two equations should be proportional.
Analysis of Conditions:
- If k = 6, the coefficients of x in the two equations are 6 and 2, which are not proportional, so the lines intersect.
- If k ≠ 6, the coefficients of x in the two equations are k and 2, which are not proportional, so the lines intersect.
- If k = 0, the first equation becomes 3y + 1 = 0, which is a horizontal line, and the second equation becomes 2x + y + 3 = 0, which is a slant line, so they intersect.
- If k ≠ 0, the lines intersect as shown in the previous conditions.
Correct Answer:
Therefore, the correct answer is option 'B' (k ≠ 6) because for any value of k other than 6, the given pair of linear equations will intersect each other.
Intersection of Linear Equations:
When two linear equations intersect each other, it means they have a common solution, which is the point where the two lines representing the equations meet on the coordinate plane.
Given Equations:
The pair of linear equations is kx + 3y + 1 = 0 and 2x + y + 3 = 0.
Conditions for Intersection:
For the two equations to intersect each other, they must have a unique solution, which means they should not be parallel lines. The condition for parallel lines is that the coefficients of x and y in the two equations should be proportional.
Analysis of Conditions:
- If k = 6, the coefficients of x in the two equations are 6 and 2, which are not proportional, so the lines intersect.
- If k ≠ 6, the coefficients of x in the two equations are k and 2, which are not proportional, so the lines intersect.
- If k = 0, the first equation becomes 3y + 1 = 0, which is a horizontal line, and the second equation becomes 2x + y + 3 = 0, which is a slant line, so they intersect.
- If k ≠ 0, the lines intersect as shown in the previous conditions.
Correct Answer:
Therefore, the correct answer is option 'B' (k ≠ 6) because for any value of k other than 6, the given pair of linear equations will intersect each other.
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The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, ifa)k = 6b)k ≠ 6c)k = 0d)k ≠ 0Correct answer is option 'B'. Can you explain this answer?
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