Q. 5

# If the system of

Given:

Equation 1: 2x + 3y = 7

Equation 2: (a + b)x + (2a –b)y = 21

Both the equations are in the form of :

a1x + b1y = c1 & a2x + b2y = c2 where

a1 & a2 are the coefficients of x

b1 & b2 are the coefficients of y

c1 & c2 are the constants

For the system of linear equations to have infinitely many solutions we must have

………(i)

According to the problem:

a1 = 2

a2 = (a + b)

b1 = 3

b2 = (2a – b)

c1 = 7

c2 = 21

Putting the above values in equation (i) we get:

On cross multiplication and solving the above equalities we get two sets of linear equation with the variables a & b.

7(a + b) = 15*2 7a + 7b = 42 .......(ii)

7(2a – b) = 15*3 14a – 7b = 63 ………(iii)

Equation (ii) and (iii) are two linear equations with a and b as variables. To solve this two set of linear equations we use the elimination technique.

In the elimination technique one variable is eliminated by equating it’s coefficient with the other equation. From equation (ii) and (iii) we first eliminate the variable b and find the value of a. Since the coefficient of b are equal but of opposite signs so we add equations (ii) and (iii) On adding we get

(14 + 7)a = 42 + 63 21a = 105 a = 5

Putting the value of a in equation (ii) we get

7*5 + 7b = 42 7b = 42 – 35 b = 1

### Thevalue of a & b for which the system of equations has infinitely many solutions is a = 5 & b = 1.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Resistors in Parallel45 mins
Resistors in Parallel39 mins
Resistors in Series47 mins
Transportation in One Shot42 mins
Resistors in Series42 mins
Human Reproduction in One Shot45 mins
Extraction of Metal56 mins
Outcomes of Democracy43 mins
Refraction of Light-241 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
RELATED QUESTIONS :

Solve each of theRS Aggarwal - Mathematics

If 2x – 3y = 7 anRD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics