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Solve the following by cross multiplication method x\a+y\b=2,ax-by=a×a-b×b​

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Answer:

By cross multiplication, do you mean cross multiplication of the coefficients of the variables?

xa+yb=2

ax−by=a2−b2

Rewrite the first equation in a more beautiful form. Multiply it throughout by ab .

bx+ay=2ab

The coefficients of the variables are interchanged between the two equations. I assume that by cross multiplication, you mean making the coefficients equal, so that a simple subtraction of the equations will eliminate a variable.

Multiply the first equation by a and the second by b .

abx+a2y=2a2b

abx−b2y=a2b−b3

Subtract them.

(a2+b2)y=(a2+b2)b

⟹y=b

Substituting this value in any of the above equations will yield the value of x .

bx+ay=2ab

⟹bx+ab=2ab

⟹x=a

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Auger Brian
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