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.

Answer 1

Rewrite the inequalities:

x − 4y < 4 => −4y < 4 − x => y > (1/4)x − 1 (strict ⇒ dashed boundary, shade above)
y < x + 1 => boundary y = x + 1 (strict ⇒ dashed boundary, shade below)

So the solution is the region between the two lines: above the line through (0, −1) and (4, 0) and below the line through (−1, 0) and (0, 1). That matches the first described graph (the one shading above the (0,−1)-(4,0) line and below the (−1,0)-(0,1) line).