Q7 of 26 Page 60

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


More from this chapter

All 26 →
5

The following statement is true for line corresponding to the inequation y – 3 ≤ 0:

 6

Write the number of equations of the following pair of linear equations:

x + 2y – 8 = 0; 2x + 4y = 16

 8

Shade the solution set of the inequation |x|≤ 3.

 9

Shade the solution set of the inequality

2x + 3y ≥ 3.