In which quadrant does the solution of the system fall?
y = x - 1
y = -3x - 5
A.) I
B.) II
C.) III
D.) IV
To determine the quadrant where the solution falls, we need to find the values of x and y that satisfy both equations.
First, let's solve the system of equations by setting them equal to each other:
x - 1 = -3x - 5
Adding 3x to both sides:
4x - 1 = -5
Adding 1 to both sides:
4x = -4
Dividing both sides by 4:
x = -1
Now, let's substitute x = -1 back into either equation to find the value of y:
y = -3(-1) - 5
y = 3 - 5
y = -2
The solution to the system of equations is x = -1 and y = -2.
With this solution, we can determine the quadrant by looking at the signs of x and y. Since both x and y are negative, the solution falls in quadrant III.
Therefore, the answer is C.) III.