Question

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

Answer 1

Answer:

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

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