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Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2?
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Introduction
To find the values of P and Q for which the given system of equations has infinitely many solutions.
Explanation
The system of equations is:
(2p-1)x + 3y = 5 ---(1)
3x + (q-1)y = 2 ---(2)
To have infinitely many solutions, the two equations must be dependent, i.e., one equation must be a multiple of the other equation. We can check this by finding the ratio of the coefficients of x and y in the two equations.
Step 1: Find the ratio of coefficients of x in equations (1) and (2):
(2p-1) / 3x = 5 / 2
=> 4p - 2 = 9x
=> x = (4p - 2) / 9
Step 2: Find the ratio of coefficients of y in equations (1) and (2):
3 / (q-1) = 5 / 2
=> 6 = 5(q-1)
=> q = 11/5
Step 3: Substitute the value of q in equation (2):
3x + (11/5 - 1)y = 2
=> 3x + (6/5)y = 2
=> 3x = (10/3 - 2y)
Step 4: Substitute the value of x from Step 1 in the above equation:
4p - 2 = 9x
=> 4p - 2 = 4p - 2
Since the equation is true for all values of p and y, the system of equations has infinitely many solutions for q = 11/5 and any value of p.
Conclusion
The values of P and Q for which the given system of equations has infinitely many solutions are P = any real number and Q = 11/5.
To find the values of P and Q for which the given system of equations has infinitely many solutions.
Explanation
The system of equations is:
(2p-1)x + 3y = 5 ---(1)
3x + (q-1)y = 2 ---(2)
To have infinitely many solutions, the two equations must be dependent, i.e., one equation must be a multiple of the other equation. We can check this by finding the ratio of the coefficients of x and y in the two equations.
Step 1: Find the ratio of coefficients of x in equations (1) and (2):
(2p-1) / 3x = 5 / 2
=> 4p - 2 = 9x
=> x = (4p - 2) / 9
Step 2: Find the ratio of coefficients of y in equations (1) and (2):
3 / (q-1) = 5 / 2
=> 6 = 5(q-1)
=> q = 11/5
Step 3: Substitute the value of q in equation (2):
3x + (11/5 - 1)y = 2
=> 3x + (6/5)y = 2
=> 3x = (10/3 - 2y)
Step 4: Substitute the value of x from Step 1 in the above equation:
4p - 2 = 9x
=> 4p - 2 = 4p - 2
Since the equation is true for all values of p and y, the system of equations has infinitely many solutions for q = 11/5 and any value of p.
Conclusion
The values of P and Q for which the given system of equations has infinitely many solutions are P = any real number and Q = 11/5.
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Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2?
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Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2? 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 values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2?.
Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2? 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 values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the values of P and Q for which the following system of equation has infinitely many solutions: (2p-1)x+3y=5; 3x+(q-1)y=2?.
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