Question

For what values of a and b does the pair of linear equations have infinite number of solutions : 2x – 3y=7, ax + 3y=b.

Answer 1

The Given pair of  linear equation is :

2x -3y = 7……….(1)
ax + 3y = b ………….(2)

On comparing with General form of a pair of linear equations  in two variables x & y is:
a1x + b1y + c1 = 0
and   a2x + b2y + c2= 0

a1= 2 , b1= - 3, c1= - 7
a2= a, b2= 3 , c2= - b

a1/a2= 2/a , b1/b2=  -3/3, c1/c2= -7/-b = 7/b

Given: A pair of linear equations has a infinite solution, if
a1/a2 = b1/b2 = c1/c2
2/a = -3/3 = 7/b
I           II       III

Taking the first two terms
2/a = -3/3
-3a = 2× 3
-3a = 6
a = -6/3
a= -2

Taking the II and III terms

-3/3 = 7/b
-1 = 7/b
-b = 7
b = -7

Hence, the value of a = -2 & b= -7

HOPE THIS WILL HELP YOU...

Answer 2

Heya Frnd ............☺

For infinite solutions ,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

So,

$\frac{2}{a} = \: \frac{-3}{3} = \: \frac{7}{b}$

By comparing the terms ,

a = - 2

b = - 7 .................#ANS#

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HOPE IT WILL HELP YOU. . . . . . . . . . ☝⭐