Q. 34.1( 28 Votes )

# By equating coefficients of variables, solve the following equations.i. 3x - 4y = 7; 5x + 2y = 3ii. 5x + 7y = 17; 3x - 2y = 4iii. x - 2y = -10; 3x - 5y = -12iv. 4x + y = 34; x + 4y = 16

(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 Equations34 mins
NCERT | Linear Equations41 mins
Interactive session on Linear Equations in Two Variables30 mins
NCERT | Imp. Qs. on Linear Equations in Two VariablesFREE Class
Quiz | Testing Your Skills on Linear Equation in Two Variables36 mins
Quiz | Important Questions on Linear Equations In Two Variables49 mins
Champ Quiz | Do you Know about Linear Equations ?35 mins
Master Linear Equations40 mins
Problems on Linear Equations41 mins
Quiz | 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
view all courses