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# Solve Each of the Following Systems of Equations by the Method of Cross-multiplication : 57/(X + Y) + 6/(X - Y) = 5 38/(X + Y) + 21/(X - Y) = 9 - 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 :

57/(x + y) + 6/(x - y) = 5

38/(x + y) + 21/(x - y) = 9

#### Solution

Let 1/(x +y) = u and 1/(x -y ) = v Then the given system of equations become

57u + 6v = 5 => 57u + 6v - 5 = 0

38u + 21v = 9 => 38u + 21v - 9 = 0

Here

a_1 = 57, b_1 = 6, c_1 = -5

a_2 = 38, b_2 = 21, c_2 = -9

By cross multiplication, we have

=> u/(-54 + 105) = (-v)/(-513 + 190) = 1/(1193 - 228)

=> u/51 = (-v)/(-323) = 1/969

=> u/51 = v/323 = 1/969

Now

u/51= 1/969

=> u = 51/969

=> u = 1/19

And

v/(323) = 1/969

=> v = 323/969

=> v = 1/3

Now

u = 1/(x + y)

=> 1/(x + y)  =1/ 19

=>x + y = 19 ....(i)

And

v = 1/(x - y)

=> 1/(x -y) = 1/3

=> x - y = 3 ...(ii)

Now adding eq i and ii

we get x = 11

And after substituting te value x in eq (ii)

we get y = 8

Hence  the value oof x = 11 and y = 8

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Solution Solve Each of the Following Systems of Equations by the Method of Cross-multiplication : 57/(X + Y) + 6/(X - Y) = 5 38/(X + Y) + 21/(X - Y) = 9 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.
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