Choose the labelled shaded region. The four original diagrams are described equivalently by their sides of the boundary lines below.

01 / Standard#Your turn

y-2x\le4,\quad x+y\ge5,\quad y\ge2

Official paper · jm01-2022 · I.9 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Isolate y in each inequality.

Hint 2

A boundary is included when equality is allowed.

Worked solution

Convert the system to vertical comparisons.
$y\le2x+4,\quad y\ge5-x,\quad y\ge2$
This is the region above both lower boundaries and below the rising line: IV.

D: region IV.

Checks and common pitfalls: All three conditions must hold simultaneously.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Convert the system to vertical comparisons.
$y\le2x+4,\quad y\ge5-x,\quad y\ge2$
This is the region above both lower boundaries and below the rising line: IV.

Think first. Reveal a hint when the class is ready.

2022 JM01