Question

Find the value of a and b for which the pair of linear equations has infinity many solutions : 2x +y. -5 = 0 , (a + b)x + (5a + 7b)y - 20 = 0

Answer 1

Answer:

a = 12 and b = -8

Step-by-step explanation:

2x + y - 5 = 0

(a + b)x + (5a + 7b)y -20 = 0

given eq. is infinite many solution

so, a1/a2 = b1/ b2 = c1/c2

2/(a+b) = 1/(5a+7b) = -5/(-20)

2/(a+b) = 1/(5a+7b) = 1/4

on compairing

a1/a2 = c1/c2

2/(a + b) = 1/4

2 × 4 = 1(a + b)

a + b = 8 -----------------(1)

on compairing b1/b2 = c1/c2

1/(5a + 7b) = 1/4

1 × 4 = 1 × ( 5a + 7b)

5a + 7b = 4 ----------------(2)

mutiply by 5 in eq. 1

5a + 5b = 40 ----------------(3)

on subtract eq 2 from 3

5a + 5b = 40

5a + 7b = 4

- - -

..............................

-2b = 16

-b = 16/2

-b = 8

b= -8

put b in eq. 1

a + b = 4

a + (-8) = 4

a - 8 = 4

a = 4 + 8

a = 12