In which quadrant does the solution of the system fall?

Question

y = x - 1
y = -3x - 5

A.) I

B.) II

C.) III

D.) IV

Answer 1

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.