Solve the following system using substitution. What is the solution to the given system?
y = −4x −1 and 2y + 2 = −12x
(1 point)
Responses
(-1, 1)
(0, -1)
(-2, 0)
(0, 0)
To solve the system using substitution, we can start by rearranging the first equation to solve for x:
y = -4x - 1
4x = -y - 1
x = (-y - 1)/4
Now we can substitute this expression for x into the second equation:
2y + 2 = -12x
2y + 2 = -12((-y - 1)/4)
2y + 2 = -3(-y - 1)
2y + 2 = 3y + 3
2y - 3y = 3 - 2
-y = 1
y = -1
Now that we have the value of y, we can substitute it back into the first equation to solve for x:
y = -4x - 1
-1 = -4x - 1
0 = -4x
x = 0
Therefore, the solution to the given system is (0, -1).
the correct annswer
I apologize for the error in my previous response. Let's solve the system again using substitution.
We start with the first equation:
y = -4x - 1
We can substitute this expression for y into the second equation:
2y + 2 = -12x
2(-4x - 1) + 2 = -12x
-8x - 2 + 2 = -12x
-8x = -12x
4x = 0
x = 0
Now substitute the value of x into the first equation to solve for y:
y = -4(0) - 1
y = -1
Therefore, the solution to the given system is (0, -1).