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Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a?
Most Upvoted Answer
Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a?
Explanation:
Given equations:
- ax - by = a^2 + b^2
- x + y = 2a
Solution:
Step 1: Solve for y in terms of x
- From the second equation, y = 2a - x
Step 2: Substitute y into the first equation
- ax - b(2a - x) = a^2 + b^2
- ax - 2ab + bx = a^2 + b^2
- x(a + b) = a^2 + b^2 + 2ab
- x = (a^2 + b^2 + 2ab) / (a + b)
Step 3: Substitute x back into the second equation to solve for y
- y = 2a - (a^2 + b^2 + 2ab) / (a + b)
- y = (2a(a + b) - a^2 - b^2 - 2ab) / (a + b)
- y = (2a^2 + 2ab - a^2 - b^2 - 2ab) / (a + b)
- y = (a^2 - b^2) / (a + b)
Therefore, the solutions are:
- x = (a^2 + b^2 + 2ab) / (a + b)
- y = (a^2 - b^2) / (a + b)
Given equations:
- ax - by = a^2 + b^2
- x + y = 2a
Solution:
Step 1: Solve for y in terms of x
- From the second equation, y = 2a - x
Step 2: Substitute y into the first equation
- ax - b(2a - x) = a^2 + b^2
- ax - 2ab + bx = a^2 + b^2
- x(a + b) = a^2 + b^2 + 2ab
- x = (a^2 + b^2 + 2ab) / (a + b)
Step 3: Substitute x back into the second equation to solve for y
- y = 2a - (a^2 + b^2 + 2ab) / (a + b)
- y = (2a(a + b) - a^2 - b^2 - 2ab) / (a + b)
- y = (2a^2 + 2ab - a^2 - b^2 - 2ab) / (a + b)
- y = (a^2 - b^2) / (a + b)
Therefore, the solutions are:
- x = (a^2 + b^2 + 2ab) / (a + b)
- y = (a^2 - b^2) / (a + b)
Community Answer
Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a?
Answer is y = a² - b²/ a + b x = (a+b)²/a+b
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Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a? 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 Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a?.
Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a? 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 Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve for x and y : ax - by = a^2 + b^2 and x + y = 2a?.
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