Question

Choose the graph that represents the following system of inequalities:

y ≤ −3x + 1
y ≤ 1 over 2x + 3

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.
Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.
Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.
Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Answer 1

9514 1404 393

Answer:

C

Explanation:

Both inequalities have y ≤ ( ), so will be bounded by solid lines, and shaded below that line (where y-values are lower). The first inequality has a boundary line with a steeply negative slope; the second has a shallow positive slope.

Since both are shaded below, the doubly-shaded area (AB) will be in the bottom quadrant, below the point of intersection of the lines. The graph attached below shows the correct shading.