Question

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Answer 1

Question:

Solve the simultaneous equations 47x + 31y = 63 & 31x + 47y = 15.

Answer:

The solution of the given simultaneous equations is ( x, y ) = ( 2, - 1 ).

Step-by-step-explanation:

The given simultaneous equations are

47x + 31y = 63 - - - ( 1 ) &

31x + 47y = 15 - - - ( 2 )

By adding equations ( 1 ) & ( 2 ), we get,

47x + 31y + ( 31x + 47y ) = 63 + 15

⇒ 47x + 31y + 31x + 47y = 78

⇒ 78x + 78y = 78

⇒ x + y = 1 - - - [ Dividing by 78 ]

⇒ x = 1 - y

⇒ x = - y + 1

By substituting this value in equation ( 2 ), we get,

31x + 47y = 15 - - - ( 2 )

⇒ 31 * ( - y + 1 ) + 47y = 15

⇒ - 31y + 31 + 47y = 15

⇒ 16y = 15 - 31

⇒ 16y = - 16

⇒ y = - 16 ÷ 16

⇒ y = - 1

Now,

x = - y + 1

⇒ x = - ( - 1 ) + 1

⇒ x = 1 + 1

⇒ x = 2

∴ The solution of the given simultaneous equations is ( x, y ) = ( 2, - 1 ).