Given the equation 3x+9y= -8, write a second linear equation to create a system that: has infinitely many solutions. explain your reasoning

To have infinitely many solutions the two equations have to describe the same line, the same slope and the same y-intercept...So any multiple of the original equation will give two lies that have infinitely many solutions, because they are in fact the same line...

3x+9y=-8

9y=-3x-8

y=(-3x-8)/9  now you can multiply both the numerator and denominator by any real value of x and produce a line that is the same as this line.  For example:

y=-5*(-3x-8)/(-5*9)

y=(15x+40)/(-45)  but any of the infinite possible multiples will do...