Q. 103.6( 39 Votes )

Find the relation

Answer :

Given: x = 3 and y = 1 is the solution of the given equations:


x – 4y + p = 0


and 2x + y – q – 2 = 0


To find: Relation between p and q


Proof:



On taking



-q – 2 = 2p


2p + q + 2 = 0


It is given that x = 3 and y = 1 is the solution of the equation


x – 4y + p = 0 …(i)


and 2x + y – q – 2 = 0 …(ii)


Substituting the value x = 3 and y = 1 in eq.(i), we get


(3) – 4(1) + p = 0


3 – 4 + p = 0


-1 + p = 0


p = 1


So, eq. (i) become


x – 4y + 1 = 0


Substituting the value x = 3 and y = 1 in eq.(ii), we get


2(3) + (1) – q – 2 = 0


6 + 1 – q – 2 = 0


-q + 5 = 0


q = 5


So, eq. (ii) become


2x + y – 5 – 2 = 0


or 2x + y – 7 = 0


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