Q. 34.1( 28 Votes )

By equating coefficients of variables, solve the following equations.

i. 3x - 4y = 7; 5x + 2y = 3

ii. 5x + 7y = 17; 3x - 2y = 4

iii. x - 2y = -10; 3x - 5y = -12

iv. 4x + y = 34; x + 4y = 16

Answer :

(i)


3x - 4y = 7 eq.[1]


5x + 2y = 3 eq.[2]


Multiplying eq.[2] by 2 both side, we get


10x + 4y = 6 eq.[3]


Adding eq.[1] and eq.[3], we get


3x - 4y + 10x + 4y = 7 + 6


13x = 13


x = 1


Putting this in eq.[1], we get


3(1) - 4y = 7


-4y = 7 - 3


-4y = 4


y = -1


(ii)


5x + 7y = 17 eq.[1]


3x - 2y = 4 eq.[2]


Multiplying eq.[1] by 3 both side and Multiplying eq.[2] by 5 both side we get,


15x + 21y = 51 eq.[3]


15x - 10y = 20 eq.[4]


Subtracting eq.[4] from eq.[3], we get


15x + 21y - 15x + 10y = 51 - 20


31y = 31


y = 1


Putting this in eq.[1], we get


5x + 7(1) = 17


5x = 10


x = 2


(iii)


x - 2y = -10 eq.[1]


3x - 5y = -12 eq.[2]


Multiplying eq.[1] by 3


3x - 6y = -30 eq.[3]


Subtracting eq.[2] from eq.[3], we get


3x - 6y - 3x + 5y = -30 + 12


-y = -18


y = 18


Putting this in eq.[1], we get


x - 2(18) = -10


x - 36 = -10


x = 26


(iv)


4x + y = 34 eq.[1]


x + 4y = 16 eq.[2]


Multiplying eq.[2] by 4 both side, we get


4x + 16y = 64 eq.[3]


Subtracting eq.[3] from eq.[1], we get


4x + 16y - 4x - y = 64 - 34


15y = 30


y = 2


Putting this in eq.[2], we get


x + 4(2) = 16


x + 8 = 16


x = 8


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Goprep Genius Quiz on Linear EquationsGoprep Genius Quiz on Linear EquationsGoprep Genius Quiz on Linear Equations34 mins
NCERT | Linear EquationsNCERT | Linear EquationsNCERT | Linear Equations41 mins
Interactive session on Linear Equations in Two VariablesInteractive session on Linear Equations in Two VariablesInteractive session on Linear Equations in Two Variables30 mins
NCERT |  Imp. Qs. on Linear Equations in Two VariablesNCERT |  Imp. Qs. on Linear Equations in Two VariablesNCERT | Imp. Qs. on Linear Equations in Two VariablesFREE Class
Quiz | Testing Your Skills on Linear Equation in Two VariablesQuiz | Testing Your Skills on Linear Equation in Two VariablesQuiz | Testing Your Skills on Linear Equation in Two Variables36 mins
Quiz | Important Questions on Linear Equations In Two VariablesQuiz | Important Questions on Linear Equations In Two VariablesQuiz | Important Questions on Linear Equations In Two Variables49 mins
Champ Quiz | Do you Know about Linear Equations ?Champ Quiz | Do you Know about Linear Equations ?Champ Quiz | Do you Know about Linear Equations ?35 mins
Master Linear EquationsMaster Linear EquationsMaster Linear Equations40 mins
Problems on Linear EquationsProblems on Linear EquationsProblems on Linear Equations41 mins
Quiz | Imp. Qs. on Linear EquationsQuiz | Imp. Qs. on Linear EquationsQuiz | Imp. Qs. on Linear Equations44 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