Question

solve the following pairs of equations by reducing them to a pair of linear eqyatuons​

Answer 1

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i hope the answer is correct.

Answer 2

Question:

Solve the following pairs of equations by reducing them to a pair of linear equations.

( 1 / 2x ) + ( 1 / 3y ) = 2

( 1 / 3x ) + ( 1 / 2y ) = 13 / 6

Answer:

The solution of the given equations is

( x, y ) = ( 1 / 2, 1 / 3 ).

Step-by-step-explanation:

The given linear equations are

( 1 / 2x ) + ( 1 / 3y ) = 2 - - - ( 1 ) &

( 1 / 3x ) + ( 1 / 2y ) = 13 / 6 - - - ( 2 )

By substituting 1 / x = a and 1 / y = b, equation ( 1 ) becomes

( 1 / 2 ) a + ( 1 / 3 ) b = 2

⇒ ( a / 2 ) + ( b / 3 ) = 2

⇒ ( 3a + 2b ) / ( 2 * 3 ) = 2

⇒ ( 3a + 2b ) / 6 = 2

⇒ 3a + 2b = 2 * 6

⇒ 3a + 2b = 12

⇒ 2b = 12 - 3a

⇒ b = ( 12 - 3a ) / 2 - - - ( 3 )

By substituting 1 / x = a and 1 / y = b, equation ( 2 ) becomes

( 1 / 3 ) a + ( 1 / 2 ) b = 13 / 6

⇒ ( a / 3 ) + ( b / 2 ) = 13 / 6

⇒ ( 2a + 3b ) / ( 2 * 3 ) = 13 / 6

⇒ ( 2a + 3b ) / 6 = 13 / 6

⇒ 2a + 3b = 13 / 6 * 6

⇒ 2a + 3b = 13

⇒ 2a + 3 ( 12 - 3a ) / 2 = 13 - - - [ From ( 3 ) ]

⇒ 2a + ( 36 - 9a ) / 2 = 13

⇒ ( 4a + 36 - 9a ) / 2 = 13

⇒ 4a - 9a + 36 = 13 * 2

⇒ - 5a + 36 = 26

⇒ 36 - 26 = 5a

⇒ 10 = 5a

⇒ a = 10 / 5

⇒ a = 2

By substituting a = 2 in equation ( 3 ),

b = ( 12 - 3a ) / 2 - - - ( 3 )

⇒ b = ( 12 - 3 * 2 ) / 2

⇒ b = ( 12 - 6 ) / 2

⇒ b = 6 / 2

⇒ b = 3

Now,

1 / x = a

⇒ 1 / a = x

⇒ x = 1 / 2

And,

1 / y = b

⇒ 1 / b = y

⇒ y = 1 / 3

∴ The solution of the given equations is

( x, y ) = ( 1 / 2, 1 / 3 ).