In which quadrant does the solution of the system fall?
y = x – 1
y = –3x – 5
The system consists of two linear equations.
The first equation, y = x - 1, has a slope of 1 and a y-intercept of -1. This means that the line represented by this equation goes up 1 unit for every 1 unit it moves to the right.
The second equation, y = -3x - 5, has a slope of -3 and a y-intercept of -5. This means that the line represented by this equation goes down 3 units for every 1 unit it moves to the right.
To find the solution of the system, we need to find the x and y values that satisfy both equations.
Setting the equations equal to each other, we have:
x - 1 = -3x - 5
Combining like terms, we get:
4x = -4
Dividing both sides by 4, we find:
x = -1
Substituting this x value into either equation, we can solve for y:
y = -3(-1) - 5
y = 3 - 5
y = -2
So, the solution to the system is (x, y) = (-1, -2).
In the coordinate plane, the point (-1, -2) falls in Quadrant III (to the left and below the origin).