Question

The value of a and b for which the following system of linear equation has infinite number of solution 2x+y-5=0;(a+b)x+(a-2b)y-15=0

Answer 1

to find b,
2a+2b=12
2(5)+2b=12
10+2b=12
2b=12-10=2
b=2/2=1
therefore,
a=5 b=1
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Answer 2

Answer:

a = -5

b =-1

Step-by-step explanation:

The equations are

2x−3y−7=0

a1 = 2 , b1 = -3 , c1 = -7

(a+b)x−(a+b−3)y−(4a+b)=0

a2=(a+b) , b2=(a+b-3) , c=(4a+b)

The system of linear equation has infinite solutions

∴ a1/a2 = b1/b2 = c1/c2

⇒ 2/a+b= -3/−(a+b−3) = -7/−(4a+b)

⇒ 2/(a+b)= 3/(a+b−3)

⇒2a+2b−6=3a+3b

⇒b=−a−6

Again, we have

⇒ 3/(a+b−3) = 7/(4a+b)

⇒12a+3b=7a+7b−21

⇒5a−4b=−21

Putting b=−a−6

⇒5a−4(−a−6)=−21⇒9a=−45

⇒a=−5

Putting a=−5inb=−a−6

⇒b=−(−5)−6⇒b=−1

⇒a=−5,b=−1

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