Answer :

(i)


Let and , then the equations becomes.




Using cross-multiplication method, we obtain,





p = 2 and q = 3

Note: These questions can also be solved by elimination method and the substitution method.
In the elimination method, the coefficient of one variable in both equations is made the same by multiplying the equation and the variable is eliminated.
In the substitution method, the value of one variable is calculated in terms of another variable by equation one and then that value is put into another equation. 



(ii) Putting in the given equations, we obtain


2p +3q = 2........(i)


4p - 9q = -1 .......(ii)


Multiplying equation (1) by 3,


we obtain 6p + 9q = 6....... (iii)


Adding equation (ii) and (iii), we obtain


10p = 5



Putting in equation (i), we obtain


=


= 3q = 1


=


p =


=


q =


=


Hence, x = 4 and y = 9.


(iii) Putting


= 4p + 3y = 14


= 4p + 3y - 14 = 0.....................(i)


And, 3p - 4y = 23


= 3p - 4y -23 = 0.......................(ii)


By cross- multiplication , we get,


=


=


Now,


=


=


Also, p =


Hence, x =


(iv) Putting


= 5p + q = 2....................(i)


= 6p - 3q = 1 .....................(ii)


Now, multiplying equation (i) by 3 we get,


= 15p + 3q = 6..............(iii)


Adding equations (ii) and (iii)


21 p = 7


= p =


Putting value of p in equation (iii) we get,


=


=


= q =


We know that,


p =


= 3 = x - 1


= x = 4


And, q =


= y - 2 = 3


= y = 5


Hence, x = 4 and y = 5


(v)


=


=


=


Putting  in (i) and (ii) to get, 


7q - 2p = 5 ................(iii)


8q + 7p = 15 .................(iv)


multiplying equation (iii) by 7 and equation (iv) by 2 . we get,


49q - 14p = 35.................(v)


16q + 14p = 30..................(vi)


After adding equations (v) and (vi) . we get,


65q = 65


= q = 1


Putting value of q in equation (iv) , we get,


8 + 7p = 15


= 7p = 15 - 8 = 7


= p = 1


Now,


p =


q =


Hence , x = 1 and y = 1


(vi) 6x + 3y = 6xy



2x + 4y = 5xy



Putting


6q + 3p - 6 = 0


2q + 4p - 5 = 0


By cross multiplication method , we get,


=


=


After comparing we get,


p = 1 and q =


Now ,


p =


Hence, x = 1 and y = 2


(vii) Putting


10p + 2q - 4 = 0....................(i)


15p - 5q +2 = 0 ..................,,(ii)


By applying cross multiplication method , we get,


=


=


After comparing we get,


p =


Now,




Adding equations (iii) and (iv) we get,


2x = 6


= x =


Putting value of equation (iii) we get,


y = 2


Hence, x = 3 and y = 2


(viii) Putting


p + q =



p - q =


Adding (i) and (ii) we get,


2p =


= p =


Putting value of p in (ii) we get,


=


= q =


Now,


p =


q =


Adding equations (iii) and (iv) we get,


6x = 6


= x = 1


Putting value of x in equation (iii) we get,


3(1) + y = 4


= y = 1


Hence, x = 1 and y = 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Two Stories about FlyingTwo Stories about FlyingTwo Stories about Flying39 mins
Resistors in ParallelResistors in ParallelResistors in Parallel39 mins
Transportation in One ShotTransportation in One ShotTransportation in One Shot42 mins
Resistors in SeriesResistors in SeriesResistors in Series42 mins
Human Reproduction in One ShotHuman Reproduction in One ShotHuman Reproduction in One Shot45 mins
Extraction of MetalExtraction of MetalExtraction of Metal56 mins
Outcomes of DemocracyOutcomes of DemocracyOutcomes of Democracy43 mins
Refraction of Light-2Refraction of Light-2Refraction of Light-241 mins
Reflection of light-2Reflection of light-2Reflection of light-238 mins
Purification of MetalsPurification of MetalsPurification of Metals60 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Solve the followiNCERT - Maths Exemplar

Solve the followiNCERT - Maths Exemplar

Solve for x and yRS Aggarwal - Mathematics

Sum of the areas Mathematics - Board Papers

A man can row a bRS Aggarwal - Mathematics