Identify the solution(s) of the system of equations, if any.
-4x - 4y = 4
12y = -12x - 12
no solution
(0, -1)
(-1, 0)
infinitely many solutions
divide the second by 3 and you will see that they are the same line.
To identify the solution(s) of the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution in this case.
We are given the system of equations:
-4x - 4y = 4 .......... (equation 1)
12y = -12x - 12 .......... (equation 2)
To solve this system by substitution, we can solve one equation for one variable and substitute it into the other equation.
Let's solve equation 2 for y:
12y = -12x - 12
Divide both sides of the equation by 12:
y = (-12x - 12) / 12
Simplifying further:
y = -x - 1 .......... (equation 3)
Now we substitute equation 3 into equation 1:
-4x - 4(-x - 1) = 4
-4x + 4x + 4 = 4
The x terms cancel out, leaving us with:
4 = 4
As we can see, this equation simplifies to 4 = 4, which is a true statement. This means that the two equations represent the same line, and the two equations are dependent.
Since the two equations are dependent, they have infinitely many solutions. This means that for any value of x, we can find a corresponding y value that satisfies both equations.
So, the answer is: Infinitely many solutions.