Solve each of the following systems of equations by using the method of cross multiplication:

$\frac{5}{(x + y)} - \frac{2}{(x - y)} + 1 = 0, \frac{15}{(x + y)} + \frac{7}{(x - y)} - 10 = 0. (x \neq y, x \neq - y) .$

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Solution

$fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style over denominator negative 2 left parenthesis negative 10 right parenthesis minus 7 left parenthesis 1 right parenthesis end fraction equals fraction numerator begin display style fraction numerator 1 over denominator x minus y end fraction end style over denominator 1 left parenthesis 15 right parenthesis minus left parenthesis negative 10 right parenthesis left parenthesis 5 right parenthesis end fraction equals fraction numerator 1 over denominator 7 left parenthesis 5 right parenthesis minus left parenthesis 15 right parenthesis left parenthesis negative 2 right parenthesis end fraction fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style over denominator 20 minus 7 end fraction equals fraction numerator begin display style fraction numerator 1 over denominator x minus y end fraction end style over denominator 15 plus 50 end fraction equals fraction numerator 1 over denominator 35 plus 30 end fraction fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style over denominator 13 end fraction equals fraction numerator begin display style fraction numerator 1 over denominator x minus y end fraction end style over denominator 65 end fraction equals 1 over 65 t a k i n g space l a s t space t w o space t e r m s fraction numerator begin display style fraction numerator 1 over denominator x minus y end fraction end style over denominator 65 end fraction equals 1 over 65 fraction numerator 1 over denominator x minus y end fraction equals 1 x minus y equals 1 x equals y plus 1...................... left parenthesis 1 right parenthesis t a k i n g space f i r s t space a n d space t h i r d space t e r m fraction numerator begin display style fraction numerator 1 over denominator x plus y end fraction end style over denominator 13 end fraction equals 1 over 65 fraction numerator 1 over denominator x plus y end fraction equals 1 fifth 5 equals x plus y f r o m space e q space 1 5 equals 2 y plus 1 4 equals 2 y y equals 2 a l s o space x equals y plus 1 x equals 2 plus 1 equals 3$

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Similar questions

\frac{5}{x + y} - \frac{2}{x - y} = - 1

\frac{15}{x + y} + \frac{7}{x - y} = 10

x \neq 0

y \neq 0

x \neq y

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$2 x + y + 10 = 0.$

\frac{5}{(x + y)} - \frac{2}{(x - y)} + 1 = 0 \frac{15}{(x + y)} + \frac{7}{(x - y)} - 10 = 0 (x \neq y, x \neq - y)

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