in which quadrant does the solution of the system fall?
y = x - 1
y = -3x - 5
To find out in which quadrant the solution of the system falls, we need to solve the system of equations. Let's set the two equations equal to each other since they both solve for y:
x - 1 = -3x - 5
Now, we solve for x:
x + 3x = -5 + 1
4x = -4
x = -4 / 4
x = -1
Having found x, we can now substitute it back into either of the original equations to find y. We'll use the first one:
y = x - 1
y = (-1) - 1
y = -2
The solution to the system of equations is (-1, -2). This point is in the third quadrant, where both x and y are negative.