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Solve Each of the Following Systems of Equations by the Method of Cross-multiplication X/A = Y/B 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

ax + by = a^2 + b^2

Solution

x/a = y/b

ax + by = a^2 + b^2

Here a_1 = 1/a, b_1 = (-1)/b, c_1 = 0

a_2 = a, b_2 = b,c_2 = -(a^2 + b^2)

By cross multiplication, we get

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

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

x = ((a^2 + b^2)/b)/(b/a + a/b) = ((a^2 +b^2)/b)/((b^2 + a^2)/(ab)) = a

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

Solution is (a, b)

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