Question

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

x – 4y < 4

y < x + 1

Answer 1

Rewrite each inequality in slope-intercept form:

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

y < x + 1 (already slope-intercept, strict)

So the solution is the region above the dashed line y = (1/4)x − 1 and below the dashed line y = x + 1 (both lines are dashed because the inequalities are strict). The two lines intersect at x = −8/3, y = −5/3. A quick test point (0,0) satisfies both inequalities, so the correct graph will show the band between those two lines and include the origin.