1. **State the problem:** We are given two numbers, say $x$ and $y$, with two conditions: - Their sum is less than 2. - The difference when subtracting the second number from the first is greater than 1. 2. **Write inequalities for each statement:** - Sum less than 2: $$x + y < 2$$ - Difference greater than 1: $$x - y > 1$$ 3. **Explain the system of inequalities:** We want to find all pairs $(x,y)$ that satisfy both inequalities simultaneously. 4. **Graph interpretation:** - The line for $x + y = 2$ has a negative slope $-1$ and intercepts at $(2,0)$ and $(0,2)$. - The inequality $x + y < 2$ means the region below this line. - The line for $x - y = 1$ has slope $1$ and intercepts at $(1,0)$ and $(0,-1)$. - The inequality $x - y > 1$ means the region above this line. 5. **Matching graphs to inequalities:** - The dashed line with negative slope and shading below corresponds to $x + y < 2$. - The dashed line with positive slope and shading above corresponds to $x - y > 1$. 6. **Final answer:** The two numbers $(x,y)$ satisfy the system: $$\begin{cases} x + y < 2 \\ x - y > 1 \end{cases}$$ This system describes the solution region where the shaded areas of the two inequalities overlap on the graph.