Answer:
Infinitely many solutions.
Step-by-step explanation:
To solve the system of equation using the substitution method, the problem has already given us a solution for x:
x = -4y - 9
Using this, we can plug that into the first equation and solve for y:
3x + 12y = -27
3(-4y - 9) + 12y = -27
-12y - 27 + 12y = -27
-27 = -27
The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y. This simply means that no matter what we put in for y, the statement will always be true.
Notice that these two equations are in fact the same equation:
x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27
Since these two equations are the same, then there are infinitely many solutions.
I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:
x = -4y - 9
x + 9 = -4y
y = (-1 / 4) (x + 9)
Cheers.
