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) answer

We are given

system of equations as

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

coefficient of y in first equation is 3

coefficient of y in second equation is 2a-b

so, we get

now, we can find b from first equation

we can plug it in above equation

now, we can solve for a

we get

now, we can find b

so,

.................Answer

a 360 degree rotation

step-by-step explanation: