Question

4a+3b=18;3a+2b=5


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Answer 1

Answer:

The solution of the given linear equations is ( a, b ) = ( - 21, 34 ).

Step-by-step-explanation:

The given simultaneous equations are

4a + 3b = 18 - - - ( 1 )

3a + 2b = 5 - - - ( 2 )

By subtracting equation ( 2 ) from equation ( 1 ), we get,

4a + 3b - ( 3a + 2b ) = 18 - 5

⇒ 4a + 3b - 3a - 2b = 13

⇒ 4a - 3a + 3b - 2b = 13

⇒ a + b = 13

⇒ a = 13 - b

⇒ a = - b + 13

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

3a + 2b = 5 - - - ( 2 )

⇒ 3 * ( - b + 13 ) + 2b = 5

⇒ - 3b + 39 + 2b = 5

⇒ - 3b + 2b = 5 - 39

⇒ - b = - 34

⇒ b = 34

By using this value, we get,

a = - b + 13

⇒ a = - 34 + 13

⇒ a = - 21

∴ The solution of the given linear equations is ( a, b ) = ( - 21, 34 ).