Step 1) Solve the second equation for #x#:
#9 - x = 3y#
#9 - color(red)(9) - x = 3y - color(red)(9)#
#0 - x = 3y - 9#
#-x = 3y - 9#
#color(red)(-1) * -x = color(red)(-1)(3y - 9)#
#x = (color(red)(-1) * 3y) - (color(red)(-1) * 9)#
#x = -3y - (-9)#
#x = -3y + 9#
Step 2) Substitute #(-3y + 9)# for #x# in the first equation and solve for #y#:
#4x + 12y = 36# becomes:
#4(-3y + 9) + 12y = 36#
#(4 * -3y) + (4 * 9) + 12y = 36#
#-12y + 36 + 12y = 36#
#-12y + 12y + 36 = 36#
#36 = 36#
This indicates this equation is true for every value of #y#.
Therefore for each and every point #(x, y)# which is a solution for the first equation it is also a solution for the second equation. Meaning there is an infinite number of solutions for this equation.
This, by definition, means the two equations are just different forms of an equation for the same line.
