Question

Which graph shows the solution to the system of linear equations?

y equals one third times x

x + 3y = −6

(coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1)
(coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1)
(coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1)
(coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3)

Answer 1

the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Explanation:

The system of linear equations can be written as:

y = (1/3)x

x + 3y = -6

To graph the system, we can graph each equation and find the point of intersection of the two lines.

The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).

The second equation can be written as:

y = (-1/3)x - 2

This has a slope of -1/3 and y-intercept of -2.

To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.

To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.

The graphs of the two equations intersect at the point (-3,-1).

Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).