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Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution
Most Upvoted Answer
Find the value of p for which the pair of linear equations 2px+3y=7 , ...
2px+3y=7---(1).
2x+y=6---(2).
for having exactly one solution--->
a1/a2 is not equal to b1/b2,
2p/2 is not equal to 3/1,
p is not equal to 3
2x+y=6---(2).
for having exactly one solution--->
a1/a2 is not equal to b1/b2,
2p/2 is not equal to 3/1,
p is not equal to 3
Community Answer
Find the value of p for which the pair of linear equations 2px+3y=7 , ...
Introduction:
To find the value of p for which the pair of linear equations 2px 3y=7 , 2x y=6 has exactly one solution.
Solution:
Let's write the given equations in the standard form y = mx + c, where m is the slope and c is the y-intercept.
2px - 3y = 7 => y = (2px - 7)/3
2xy - 6 = 0 => y = 3/x
Now we equate both the equations to get the value of p.
(2px - 7)/3 = 3/x
2px - 7 = 9p/x
2px^2 - 7x = 9p
2p(x^2 - 9/2) = 7x
For the given pair of equations to have exactly one solution, the discriminant of the quadratic should be zero.
b^2 - 4ac = 0
7^2 - 4(2p)(-9/2) = 0
49 + 18p = 0
p = -49/18
Explanation:
When we equated the two equations, we got a quadratic equation. For this quadratic to have only one root, the discriminant should be zero. We solved for p and got the value of p to be -49/18. This is the value for which the given pair of linear equations will have exactly one solution.
Conclusion:
The value of p for which the given pair of linear equations 2px 3y=7 , 2x y=6 has exactly one solution is -49/18.
To find the value of p for which the pair of linear equations 2px 3y=7 , 2x y=6 has exactly one solution.
Solution:
Let's write the given equations in the standard form y = mx + c, where m is the slope and c is the y-intercept.
2px - 3y = 7 => y = (2px - 7)/3
2xy - 6 = 0 => y = 3/x
Now we equate both the equations to get the value of p.
(2px - 7)/3 = 3/x
2px - 7 = 9p/x
2px^2 - 7x = 9p
2p(x^2 - 9/2) = 7x
For the given pair of equations to have exactly one solution, the discriminant of the quadratic should be zero.
b^2 - 4ac = 0
7^2 - 4(2p)(-9/2) = 0
49 + 18p = 0
p = -49/18
Explanation:
When we equated the two equations, we got a quadratic equation. For this quadratic to have only one root, the discriminant should be zero. We solved for p and got the value of p to be -49/18. This is the value for which the given pair of linear equations will have exactly one solution.
Conclusion:
The value of p for which the given pair of linear equations 2px 3y=7 , 2x y=6 has exactly one solution is -49/18.
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Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution
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Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution.
Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of p for which the pair of linear equations 2px+3y=7 , 2x+y=6 has exactly one solution.
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