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I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12
the second equation is 4/x+2 +3/y+2=17/12
and we have to find x and y?
the second equation is 4/x+2 +3/y+2=17/12
and we have to find x and y?
Most Upvoted Answer
I have a query about maths ch 3 pair of linear equations in two variab...
Understanding the Problem
You are given two equations involving variables x and y:
1. 5/(x + 2) + 7/(y + 2) = 31/12
2. 4/(x + 2) + 3/(y + 2) = 17/12
The goal is to find the values of x and y.
Substitution Method
1. Let a = x + 2
2. Let b = y + 2
This transforms the equations into:
- 5/a + 7/b = 31/12
- 4/a + 3/b = 17/12
Finding a and b
1. Multiply the first equation by 12ab:
- 60b + 84a = 31ab
2. Multiply the second equation by 12ab:
- 48b + 36a = 17ab
Now, you have two new equations:
- 60b + 84a = 31ab
- 48b + 36a = 17ab
Rearranging the Equations
1. Rearranging the first equation:
- 31ab - 60b - 84a = 0
2. Rearranging the second equation:
- 17ab - 48b - 36a = 0
Now, you can isolate one variable in terms of the other.
Solving the Equations
1. Solve one of the equations for a or b.
2. Substitute back into either equation to find the second variable.
Once you have the values of a and b, substitute back to find x and y:
- x = a - 2
- y = b - 2
Conclusion
By following the above steps and solving the equations systematically, you will obtain the values of x and y. Make sure to check your solutions by substituting back into the original equations.
You are given two equations involving variables x and y:
1. 5/(x + 2) + 7/(y + 2) = 31/12
2. 4/(x + 2) + 3/(y + 2) = 17/12
The goal is to find the values of x and y.
Substitution Method
1. Let a = x + 2
2. Let b = y + 2
This transforms the equations into:
- 5/a + 7/b = 31/12
- 4/a + 3/b = 17/12
Finding a and b
1. Multiply the first equation by 12ab:
- 60b + 84a = 31ab
2. Multiply the second equation by 12ab:
- 48b + 36a = 17ab
Now, you have two new equations:
- 60b + 84a = 31ab
- 48b + 36a = 17ab
Rearranging the Equations
1. Rearranging the first equation:
- 31ab - 60b - 84a = 0
2. Rearranging the second equation:
- 17ab - 48b - 36a = 0
Now, you can isolate one variable in terms of the other.
Solving the Equations
1. Solve one of the equations for a or b.
2. Substitute back into either equation to find the second variable.
Once you have the values of a and b, substitute back to find x and y:
- x = a - 2
- y = b - 2
Conclusion
By following the above steps and solving the equations systematically, you will obtain the values of x and y. Make sure to check your solutions by substituting back into the original equations.
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I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y?
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I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y? 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 I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y?.
I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y? 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 I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for I have a query about maths ch 3 pair of linear equations in two variables where the first equation is 5/ x+2 +7/y+2=31/12the second equation is 4/x+2 +3/y+2=17/12and we have to find x and y?.
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