Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.
A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

1. The system of inequalities that matches the graph is defined as follows:
• y ≤ 3x.
• y > –2x – 1.

### How to define the system of inequalities?

The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.
This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:
y ≤ 3x
he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.
When x increased by 3, y decayed by 6, hence the slope of the line is of:
m = -6/3 = -2.
Then:
y = -2x + b.
When x = 1, y = -3, then the intercept is given as follows:
-3 = -2 + b
b = -1.
Thus the constraint is of:
y > –2x – 1.
More can be learned about a system of inequalities at https://brainly.com/question/9290436
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