Question

for what values of a and b does the following pair of linear equations have an infinite number of solutions (i) 2x+3y=9 and (a+b)x + (2a-b)y=3(a+b+1) please answer urgent!!

Answer 1

We are given

system of equations as

`2x+3y=9`

`(a+b)x + (2a-b)y=3(a+b+1)`

It will have infinite solution when both equations will become same

so, we will set coefficients of x and y of both terms equal

We can see

coefficient of x in first equation is 2

coefficient of x in second equation is a+b

so, we get

`a+b=2`

coefficient of y in first equation is 3

coefficient of y in second equation is 2a-b

so, we get

`2a-b=3`

now, we can find b from first equation

`a+b=2`

`b=2-a`

we can plug it in above equation

`2a-(2-a)=3`

now, we can solve for a

we get

`a=(5)/(3)`

now, we can find b

`b=2-(5)/(3)`

`b=(1)/(3)`

so,

`a=(5)/(3)`

`b=(1)/(3)`.................Answer