Question

How many solutions does this system of equations have?

x-3y=6

9y=3x-18

Answer 1

??

Answer 2

rearrange the first equation
x-3y=6 => x-3y-6=0
Consider the second equation
9y=3x-18 => 3x-9y-18=0
Take out 3 as the common factor and divide both sides by 3
3(x-3y-6) =0
x-3y-6 =0
So you'll get 2 same equations
That means they are the same straight line, which have infinitely many solutions

Answer 3

How many solutions does this system of equations have?

x-4y=13

5x-20y=63