Question: Two aquifers have combined flow rates modeled by the equations $ y = 3x + 15 $ and $ y = -2x + 40 $. Find their intersection point.

Sat, 09 May 2026 07:14:57 +0000

**Answer** Two aquifers are often modeled using linear equations to predict groundwater flow and interaction—a critical concern for resource planning, especially as water scarcity grows across the U.S. Recent conversations among hydrologists and environmental planners increasingly focus on how shared water systems influence regional sustainability. The intersection point of equations describing two aquifers’ flow rates offers a tangible way to understand how these underground water bodies connect and respond to environmental changes. **Why This Question Is Gaining Attention in the U.S.**
In drought-prone regions like the Southwest and California, understanding aquifer dynamics is no longer academic. Water managers, farmers, and policymakers rely on precise models to assess how aquifers recharge, share resources, and affect long-term availability. The intersection of these two modeled flow lines reveals how two distinct aquifers interact—whether feeding into one another or representing separate but connected zones—helping inform sustainable management decisions in an era of climate uncertainty. **How the Intersection Is Found**
To find where the two aquifers’ modeled flows meet, set the equations equal:
$ 3x + 15 = -2x + 40 $
Solve for $ x $ by adding $ 2x $ to both sides and subtracting 15:
$ 5x = 25 $ → $ x = 5 $
Substitute back into one original equation, say $ y = 3x + 15 $:
$ y = 3(5) + 15 = 30 $
Thus, the intersection point is $ (5, 30) $. This mathematical meeting point reflects a balanced flow state where both aquifers’ modeled contributions converge—geometrically and functionally.