Question

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

x – 4y < 4

y < x + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

Answer 1

Solve each for y:

x − 4y < 4 => −4y < 4 − x => y > (1/4)x − 1
y < x + 1

So the boundary y = (1/4)x − 1 is dashed and the region above it is shaded; the boundary y = x + 1 is dashed and the region below it is shaded. The choice that matches the shading (above the line through (0,−1),(4,0) and below the line through (−1,0),(0,1)) is the first description. (Strict inequalities mean both lines should be dashed.)