Question

"Think about the graphs of the equations in the following system:

x = 2
y = 2 - 3x

Which of the following describes the system?

A) A circle with its center at (0, 0) and a radius of √2; a parabola opening up with its vertex at (0, -3).
B) A circle with its center at (0, 0) and a radius of √2; a parabola opening up with its vertex at (0, 3).
C) A circle with its center at (0, 0) and a radius of 2; a parabola opening up with its vertex at (0, -3).
D) A circle with its center at (0, 0) and a radius of 2; a parabola opening up with its vertex at (0, 3).

Select the description that correctly characterizes the system of equations."

Answer 1

The system of equations x = 2 and y = 2 - 3x actually describes a vertical line and a decreasing linear function, not a circle and a parabola as suggested in the answer choices.

Step-by-step explanation:

When considering the system of equations given as x = 2 and y = 2 - 3x, we must first recognize that the equation x = 2 describes a vertical line that passes through the point (2, 0) and is parallel to the y-axis. This is not a circle as described in the provided answer choices. The second equation, y = 2 - 3x is in the form of y = mx + b, where m is the slope and b is the y-intercept. This equation represents a linear function with a slope of -3 and a y-intercept of 2, meaning the line slopes downward as it moves to the right and crosses the y-axis at the point (0, 2). This is also not a parabola. Hence, none of the provided descriptions correctly characterizes the system of equations as none describe the actual shapes represented by the equations. The correct characterization of the system would be a vertical line and a decreasing linear function.