Mathematics
Grade-8
Easy

Question

Solve the following pair of equations.
2 over x plus 3 over y equals 13 space a n d space 5 over x minus 4 over y equals negative 2

  1. x equals 2 over 5 space a n d space y space equals space 1 half
  2. x equals 1 half space a n d space y equals 1 third
  3. x equals 2 over 7 space a n d space y equals 1 half
  4. x equals 2 over 5 space a n d space y equals 1 over 7

The correct answer is: x equals 1 half space a n d space y equals 1 third


    2 over x space plus space 3 over y space equals space 13 space c a n space a l s o space b e space w r i t t e n space a s space 2 y space plus space 3 x space equals space 13 x y space bold left parenthesis bold 1 bold right parenthesis
bold 5 over bold x minus space 4 over y space equals space minus 2 space c a n space a l s o space b e space w r i t t e n space a s space 5 y space minus 4 x space equals space minus 2 x y space bold left parenthesis bold 2 bold right parenthesis
bold italic M bold italic u bold italic l bold italic t bold italic i bold italic p bold italic l bold italic y bold italic i bold italic n bold italic g bold space bold 5 bold space bold italic i bold italic n bold space bold italic e bold italic q bold italic u bold italic a bold italic t bold italic i bold italic o bold italic n bold space bold 1 bold space bold italic a bold italic n bold italic d bold space bold 2 bold space bold italic i bold italic n bold space bold italic e bold italic q bold italic u bold italic a bold italic t bold italic i bold italic o bold italic n bold space bold 2 bold comma bold space bold italic w bold italic e bold space bold italic g bold italic e bold italic t bold space bold colon
10 y space plus space 15 x space equals space 65 x y space bold left parenthesis bold 3 bold right parenthesis
10 y space minus space 8 x space equals space minus 4 x y space bold left parenthesis bold 4 bold right parenthesis
bold italic S bold italic u bold italic b bold italic t bold italic r bold italic a bold italic c bold italic t bold italic i bold italic n bold italic g bold space bold 3 bold space bold italic a bold italic n bold space bold 4 bold space bold italic w bold italic e bold space bold italic g bold italic e bold italic t
23 x space equals space 69 x y
y space equals space 1 third
bold italic S bold italic u bold italic b bold italic s bold italic t bold italic i bold italic t bold italic u bold italic t bold italic i bold italic n bold italic g bold space bold italic t bold italic h bold italic e bold space bold italic v bold italic a bold italic l bold italic u bold italic e bold space bold italic o bold italic f bold space bold italic y bold space bold italic i bold italic n bold space bold italic e bold italic q bold italic u bold italic a bold italic t bold italic i bold italic o bold italic n bold space bold 1 bold space bold comma bold space bold italic w bold italic e bold space bold italic g bold italic e bold italic t bold colon
x space equals space 1 half
T h u s comma space x space equals space 1 half space a n d space y space equals space 1 third

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