Mathematics
Grade-8
Easy

Question

-2x – 5y = 10
-x – y = -1

  1. 5, 4
  2. -5, 4
  3. 5, -4
  4. -4, -5

hintHint:

  1. The Linear Combination Method , aka The Addition Method , aka The Elimination Method. Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the x -terms or the y -terms cancel out. Then solve for x (or y , whichever's left) and substitute back to get the other coordinate.

The correct answer is: 5, -4


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minus 2 x space – space 5 y space equals space 10 space 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 x plus 5 y space equals space minus 10 space space space space space......... space space space space bold left parenthesis bold italic a bold right parenthesis
minus x space – space y space equals space minus 1 space c a n space a l s o space b e space w r i t t e n space a s space x plus y space equals 1 space space space space space space space space space space space space space space space space space space space space.......... space space space bold left parenthesis bold italic b 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 2 bold space bold italic o 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 left parenthesis bold italic b bold right parenthesis bold comma
2 space cross times left parenthesis x plus y space equals 1 right parenthesis space equals space 2 x space plus space 2 y space equals 2 space space space space space............ space bold left parenthesis bold italic c 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 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 left parenthesis bold italic a bold right parenthesis bold space bold italic a bold italic n bold italic d bold space bold left parenthesis bold italic c bold right parenthesis
bold space bold space bold space bold space bold space bold space bold space bold space bold space 2 x space plus space 5 y space equals space minus 10
minus
space space space space space space space space space space 2 x space plus space 2 y space equals space 2
space space space space space space space _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
equals space space space space space space 0 space plus space 3 y space equals space minus 12
equals space space space space space space space space space y space equals space minus 4
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 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 a bold italic n bold italic y 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 italic e bold italic i bold italic t bold italic h bold italic e bold italic r bold space bold left parenthesis bold italic a bold right parenthesis bold space bold italic o bold italic r bold space bold left parenthesis bold italic b bold right parenthesis bold comma bold space bold italic w bold italic e bold space bold italic g bold italic e bold italic t
x space equals space 5
T h u s space comma space left parenthesis x comma y right parenthesis space equals space left parenthesis 5 comma negative 4 right parenthesis

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