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Solve the following system of inequalities graphically on set of axes below. State the coordinates of a point in the solution set. ​

Solve the following system of inequalities graphically on set of axes below. State-example-1

1 Answer

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Answer:

see below for a graph

(-8, 4) is in the solution set

Explanation:

You want the graph and a solution point for the inequalities y ≤ -6/5x -4 and y ≥ 2/5x +4.

Graph

The solid boundary line of the first inequality will cross the y-axis at -4, and will have a "rise" of -6 units for each "run" of 5 units. Shading is below this boundary line.

The solid boundary line of the second inequality will cross the y-axis at +4 and will have a "rise" of 2 units for each "run" of 5 units. Shading is above this boundary line.

Solution set

The boundary lines make an X shape on the graph, crossing at the point (-5, 2). The solution set is in the left quadrant.

Point (-5, 2) is in the solution set, as are points in the doubly-shaded space to its left. (-8, 4) is one of those.

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Additional comment

The boundary lines are solid because the "or equal to" case is included in each.

The ≤ symbol tells you y-values that satisfy the first inequality will be less than (or equal to) those on the boundary line.

The ≥ symbol tells you y-values that satisfy the second inequality will be greater than (or equal to) those on the boundary line.

Solve the following system of inequalities graphically on set of axes below. State-example-1
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