JAMB Mathematics 2023 Paper

Concept: Determine the boundary line from its intercepts, then use a test point to find the correct inequality sign.Explanation:The boundary line passes through $(5,0)$ and $(0,4)$. Its slope is $m = \frac{4-0}{0-5} = -\frac{4}{5}$. The $y$-intercept is $4$, so the equation is $y = -\frac{4}{5}x + 4$. Rearranging gives $y + \frac{4}{5}x = 4$. Multiply through by $5$: $5y + 4x = 20$. Use the test point $(0,0)$, which lies in the shaded region: $5(0) + 4(0) = 0 \leq 20$. Since the statement is true, the shaded region satisfies $5y + 4x \leq 20$.Answer: B. $5y + 4x \leq 20$