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Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
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Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
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Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
Solving x/a y/b=2 and ax-by=a square- b square
Step 1: Cross-multiply x/a y/b=2 to eliminate fractions
To eliminate the fractions in the first equation, we can cross-multiply both sides by the denominators:
x/a * a/b = 2 * a/b
After simplification:
xb = 2a
So, the first equation can be written as:
xb = 2a
Step 2: Simplify the second equation
Now, let's simplify the second equation:
ax - by = a^2 - b^2
We can rewrite this equation as:
ax - a^2 = by - b^2
Factor out a from the left-hand side and b from the right-hand side:
a(x - a) = b(b - y)
So, the second equation can be written as:
a(x - a) = b(b - y)
Step 3: Solve for y in terms of x
Now, let's solve for y in terms of x:
xb = 2a
y = (2a - bx) / b
Step 4: Substitute y into the second equation
Substituting y into the second equation:
a(x - a) = b(b - (2a - bx) / b)
Simplifying:
a(x - a) = b^2 - 2a + bx
Expanding:
ax - a^2 = b^2 - 2a + bx
Bringing all the terms to one side:
bx - ax + a^2 - b^2 + 2a = 0
Simplifying:
(b - a)x + (a + b)(a - b) = 0
Factor out (b - a):
(b - a)(x - (a + b)) = 0
Step 5: Solve for x and y
So, the solutions are:
x = a + b or y = (2a - bx) / b
If x = a + b:
y = (2a - b(a + b)) / b = (a - b) / b
If y = (2a - bx) / b:
x = (2a - by) / b = (2a - b(2a - bx)) / b = (3a - bx) / b
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Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
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Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square 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 by cross multiplication x/a+y/b=2 and ax-by=a square- b square covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square .
Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square 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 by cross multiplication x/a+y/b=2 and ax-by=a square- b square covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square .
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