Question

Find the value of a and b for which the following pair of linear equation has infinite number of solutions 1. 2x+3y=7,ax+(a+b)y=28

Answer 1

given
equations are
2x+3y = 7
a1x +b1 y = c1
a1 = 2
b1= 3
c1 = 7

ax +(a+b)y = 28
a2x+b2y =c2

a2= a
b2 = (a+b)
c2 = 28

for infinite solution condition is

a1/a2 = b1/b2 = c1/c2

2/a = 3/(a+b) = 7/28

2/a = 1/4
a= 8

3/(a+b) = 1/4

a+b = 12

8+b = 12

b = 4

thus a = 8
b = 4

Answer 2

given

equations are

2x+3y = 7

a1x +b1 y = c1

a1 = 2

b1= 3

c1 = 7

ax +(a+b)y = 28

a2x+b2y =c2

a2= a

b2 = (a+b)

c2 = 28

for infinite solution condition is

a1/a2 = b1/b2 = c1/c2

2/a = 3/(a+b) = 7/28

2/a = 1/4

a= 8

3/(a+b) = 1/4

a+b = 12

8+b = 12

b = 4

thus a = 8

b = 4

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