# If the pair of equations 2x + 3y = 7; (a + b)x + (2a – b)y = 21 has infinitely many solutions then find the values of a, b.

Given, 2x + 3y = 7; (a + b)x + (2a – b)y = 21

We know that a pair of linear equations has infinitely many solutions

when, Here, a1 = 2, b1 = 3, c1 = 7

and a2 = (a + b), b2 = (2a – b), c2 = 21  A + b = 6 …(i) 2a – b = 9 …(ii)

Adding both the equations we get,

3a = 15

a = 5

b = 6 – 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  Dealing With the Real Life Problems53 mins  Quiz | Real Life Problems Through Linear Equations56 mins  Quiz | Solution of Linear Equations53 mins  Champ Quiz | Consistency and Inconsistency of Solutions36 mins  Pair of Linear Equations in Two Variables46 mins  Consistent and Inconsistent Equations33 mins  Elimination (quicker than quickest)44 mins  Real Life Problems Through Linear Equations41 mins  All Kinds of Word Problems in Linear Equations42 mins  Master Substitution Method46 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 :

Comparing the ratio and find out whether the following pairs of linear equations are consistent or inconsistent.

(i) 2x – 3y = 8; 4x – 6y = 9

(ii) 3x – y = 2; 6x – 2y = 4

(iii) 2x – 2y = 2; 4x – 4y = 5

(iv) Rajasthan Board Mathematics