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CBSE - X - Mathematics - Pair of Linear Equations in 2 Variables

solve the system of equation 11/v-7/u=1;9/v-4/u=6
 

Asked by tarjindersingh55 2nd October 2017, 11:57 AM
Answered by Expert

Answer:

begin mathsize 16px style Given space system space of space equations space are
11 over straight v minus 7 over straight u equals 1
9 over straight v minus 4 over straight u equals 6
Let space 1 over straight u equals straight x space and space 1 over straight v equals straight y
Then comma space we space have
11 straight x minus 7 straight y equals 1 space space space space space space space space space.... left parenthesis straight i right parenthesis
9 straight x minus 4 straight y equals 6 space space space space space space space space space space space.... left parenthesis ii right parenthesis
Multiplying space left parenthesis straight i right parenthesis space by space 9 space and space left parenthesis ii right parenthesis space by space 11 comma space we space get
99 straight x minus 63 straight y equals 9 space space space space space space space space space space.... left parenthesis iii right parenthesis
99 straight x minus 44 straight y equals 66 space space space space space space space space.... left parenthesis iv right parenthesis
Subtracting space left parenthesis iii right parenthesis space from space left parenthesis iv right parenthesis comma space we space get
19 straight y equals 57
rightwards double arrow straight y equals 3
rightwards double arrow 11 straight x minus 7 cross times 3 equals 1
rightwards double arrow 11 straight x equals 22
rightwards double arrow straight x equals 2
Thus comma space we space have
straight x equals 2 rightwards double arrow 1 over straight u equals 2 rightwards double arrow straight u equals 1 half
straight y equals 3 rightwards double arrow 1 over straight v equals 3 rightwards double arrow straight v equals 1 third

end style
Answered by Expert 3rd October 2017, 9:46 AM

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