Class 10 Exam  >  Class 10 Questions  >  Solve by cross multiplication x/a+y/b=2 and a... Start Learning for Free
Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
Most Upvoted Answer
Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
Community Answer
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
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
Explore Courses for Class 10 exam

Top Courses for Class 10

Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square
Question Description
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 .
Solutions for Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square in English & in Hindi are available as part of our courses for Class 10. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square defined & explained in the simplest way possible. Besides giving the explanation of Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square , a detailed solution for Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square has been provided alongside types of Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square theory, EduRev gives you an ample number of questions to practice Solve by cross multiplication x/a+y/b=2 and ax-by=a square- b square tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev