Question

A system of two linear inequalities in two variables is shown.

y ≥ 1 over 2x − 1

y < 4 over 3x − 2

Which graph represents the solution set of the system of inequalities?

A
Y; X;
B
Y; X;
C
Y; X;
D
Y; X;

Answer 1

First rewrite the inequalities as lines:
y ≥ (1/2)x − 1 and y < (4/3)x − 2.

Key features to look for on the correct graph:
- The line y = (1/2)x − 1 is solid (because ≥) and has y‑intercept (0, −1) and slope 1/2.
- The line y = (4/3)x − 2 is dashed (because <) and has y‑intercept (0, −2) and slope 4/3.
- The two lines intersect at x = 6/5, y = −2/5 (i.e. (1.2, −0.4)).
- The solution set is the region between the two lines for x > 6/5 (to the right of their intersection), including the lower (solid) line and excluding the upper (dashed) line.

So choose the graph that shades the band between those two lines to the right of (6/5, −2/5), with the lower line solid and the upper line dashed. If you paste the four graphs I can pick A–D for you.