-4x-4y=12
16y=-16x-48
identify the solution of the system or equatuions
-4x-4y=12
Mutliply by 4.
-16x - 16y = 48
Second equation:
16y=-16x-48
Transpose.
16x + 16y = -48
Multiply by -1.
-16x - 16y = 48
What does that tell you?
To identify the solution of the system of equations, we can use the method of substitution or elimination. Let's solve this system of equations using the method of substitution:
Given equations:
1) -4x - 4y = 12 --(equation 1)
2) 16y = -16x - 48 --(equation 2)
Step 1: Solve equation 2 for one variable in terms of the other.
Dividing both sides of equation 2 by 16, we get:
y = (-16x - 48)/16
y = -x - 3 -- (equation 3)
Step 2: Substitute the value of y from equation 3 into equation 1.
Replace y in equation 1 with -x - 3:
-4x - 4(-x - 3) = 12
Simplifying, we have:
-4x + 4x + 12 = 12
12 = 12
Step 3: Analyze the equation obtained from step 2.
Here, we reach a contradiction (0 = 12). This means that there is no specific solution for this system of equations. The equations are dependent and represent the same line. The entire line is the solution.
Therefore, the system of equations {-4x - 4y = 12, 16y = -16x - 48} does not have a specific solution. Instead, it represents a dependent system with infinitely many solutions that lie on the same line.