1. **State the problem:** We have multiple linear equations of the form $h = mx + b$ with slopes $3$, $-3$, and $1$, and intercepts $1$ and $7$. We want to identify which pairs of these equations form systems with exactly one solution. 2. **Recall the rule for one solution:** Two linear equations have exactly one solution if and only if their slopes are different. This means the lines intersect at exactly one point. 3. **List the given equations:** - $h = 3x + 1$ - $h = -3x + 7$ - $h = 3x + 7$ - $h = x + 1$ 4. **Check pairs for different slopes:** - Pair 1: $h = 3x + 1$ and $h = -3x + 7$ have slopes $3$ and $-3$ (different) $ ightarrow$ one solution. - Pair 2: $h = 3x + 1$ and $h = 3x + 7$ have slopes both $3$ (same) $ ightarrow$ no solution or infinite solutions depending on intercepts (here different intercepts, so no solution). - Pair 3: $h = 3x + 1$ and $h = x + 1$ have slopes $3$ and $1$ (different) $ ightarrow$ one solution. - Pair 4: $h = -3x + 7$ and $h = 3x + 7$ have slopes $-3$ and $3$ (different) $ ightarrow$ one solution. - Pair 5: $h = -3x + 7$ and $h = x + 1$ have slopes $-3$ and $1$ (different) $ ightarrow$ one solution. - Pair 6: $h = 3x + 7$ and $h = x + 1$ have slopes $3$ and $1$ (different) $ ightarrow$ one solution. 5. **Conclusion:** All pairs with different slopes have exactly one solution. Pairs with the same slope but different intercepts have no solution. **Final answer:** The systems with exactly one solution are all pairs of equations with different slopes: $(3x+1, -3x+7)$, $(3x+1, x+1)$, $(-3x+7, 3x+7)$, $(-3x+7, x+1)$, and $(3x+7, x+1)$.