Question

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

2x – 3y <12

y < –3

On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.

On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.

On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.

On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.

Answer 1

Rewrite 2x − 3y < 12 as y > (2/3)x − 4. So the solution is points satisfying
- y < −3 (below the horizontal line y = −3), and
- y > (2/3)x − 4 (above the sloped line through (0, −4) and (3, −2)).

That is the region between the two lines: below y = −3 and above the sloped line. This matches the third graph (horizontal dashed line y = −3 with shading below, sloped line with shading above).