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

$a=\frac{5}{3}$

now, we can find b

$b=2-\frac{5}{3}$

$b=\frac{1}{3}$

so,

$a=\frac{5}{3}$

$b=\frac{1}{3}$.................Answer