Share

# Solve Each of the Following Systems of Equations by the Method of Cross-multiplication X/A + Y/B = 2 Ax - by = A^2 - B^2 - CBSE Class 10 - Mathematics

ConceptAlgebraic Methods of Solving a Pair of Linear Equations Cross - Multiplication Method

#### Question

Solve each of the following systems of equations by the method of cross-multiplication

x/a + y/b = 2

ax - by = a^2 - b^2

#### Solution

The system of the given equations may be written as

1/a x xx + 1/b xx y - 2 = 0

ax - by + b^2 - a^2 = 0

here

a_1 = 1/a, b_1 = 1/b, c_1 = -2

a_2 = a, b_2= -b, c_2 = b^2 - a^2

By cross multiplication, we get

=> x/(1/b xx (b^2 - a^2) - (-2) xx (-b)) = (-y)/(1/a xx (b^2 - a^2) - (-2) xx a) = 1/((-bxx1)/a - (a xx1)/b)

=> x/((b^2 - a^2)/b - 2b) = (-y)/((b^2 - a^2)/b + 2b) = 1/((-b)/a - a/b)

=> x/((b^2 -a^2 - 2b^2)/b) = (-y)/((b^2 - a^2 + 2b^2)/a) = 1/((-b^2 - a^2)/(ab)

=> x/((a^2 - b^2)/b) = (-y)/((b^2 + a^2)/a) = 1/((-b^2 -a^2)/(ab)

Now

x/((-a^2 -b^2)/b) = 1/((-b^2 - a^2)/(ab)

=> x = (-a^2 - b^2)/b xx (ab)/(-b^2 - a^2)

And

(-y)/((b^2 + a^2)/a)= 1/((-b^2 -a^2)/(ab))

=> -y = (b^2 + a^2)/a xx (ab)/(-b^2 - a^2)

=> -y = ((b^2 + a^2)xxb)/(-(b^2 + a^2)

=> y = b

Hence, , x = a, y = b is the solution of the given system of the equations.

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [2]

Solution Solve Each of the Following Systems of Equations by the Method of Cross-multiplication X/A + Y/B = 2 Ax - by = A^2 - B^2 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.
S