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 ...