Question

(Time expired.) The graph shows the system of equations below.

2 x minus 3 y = negative 6. y = negative one-third x minus 4



Which statement is supported by the graph?

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

B. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is ( –2, –6).

C. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (2, –4).

D. The red line represents the equation 2x-3y=6, and the solution to the system of equations is (–4, 2).

Answer 1

A: The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

Answer 2

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).

Explanation:

Here we have the system:

2x - 3y = -6

y = -(1/3)*x - 4

First, remember that if the slope is negative, then the equation is decreasing.

So, for the second equation, as x increases, y decreases, then the line of the second equation is the red one (because the red one decreases).

So the blue one represents the equation 2x - 3y = -6

Also remember that the solution of a system of equations is the point where the graphs of the equations intersect, here we can see that the intersection happens at the point (-6, - 2)

This means that the solution of the system is (-6, - 2)

From this, we can see that the correct option is:

A. The blue line represents the equation 2x-3y=6, and the solution to the system of equations is (–6, –2).