Question:** A marine autonomous underwater geological mapping engineer is analyzing the mineral composition data from two distinct seabed regions. If $a$ represents the concentration of mineral A in grams per liter and $b$ represents the concentration of mineral B, and the engineer finds that $3a + 4b = 12$ and $a - 2b = -1$, find the concentrations $a$ and $b$.

["Title: Solving for Mineral Concentrations: A Marine Geological Mapping Engineer’s Analysis", "Meta Description:\nAn engineer analyzing mineral composition in seabed regions uses a system of equations to determine the concentrations of minerals A and B. Solve $3a + 4b = 12$ and $a - 2b = -1$ to uncover $a$ and $b$.", "---", "Understanding the mineral makeup of the seabed is critical for oceanographic research and resource exploration. In this case, a marine autonomous underwater geological mapping engineer is tasked with analyzing mineral concentrations in two distinct seabed regions. Using computational models, the engineer relies on quantitative data derived from sensor readings. Two key variables have been identified: $a$, the concentration of mineral A in grams per liter, and $b$, the concentration of mineral B. By solving a system of linear equations, the engineer can determine the precise concentrations of these minerals.", "---", "### The System of Equations", "Two equations have been established based on field data:", "1. $3a + 4b = 12$  — representing mineral equilibrium and sensor calibration\n2. $a - 2b = -1$  — modeling mineral interaction dynamics", "Solving this system accurately provides the concentrations $a$ and $b$, which are essential for geological mapping and resource assessment.", "---", "### Step-by-Step Solution", "Let’s solve the system using substitution and elimination.", "Step 1: Solve the second equation for $a$:\n$$\na - 2b = -1 \Rightarrow a = 2b - 1\n$$", "Step 2: Substitute $a = 2b - 1$ into the first equation:\n$$\n3(2b - 1) + 4b = 12\n$$\n$$\n6b - 3 + 4b = 12\n$$\n$$\n10b - 3 = 12\n\Rightarrow 10b = 15\n\Rightarrow b = 1.5\n$$", "Step 3: Substitute $b = 1.5$ back into $a = 2b - 1$:\n$$\na = 2(1.5) - 1 = 3 - 1 = 2\n$$", "---", "### Final Answer", "The concentrations of the minerals are:\n- $a = 2$ grams per liter\n- $b = 1.5$ grams per liter", "These values provide critical insight into the geochemical profile of the seabed, supporting precise geological mapping and future exploration missions.", "By accurately interpreting mineral data through mathematical modeling, marine engineers enhance our understanding of Earth’s oceanic resources—and one equation at a time.", "---", "Keywords: marine autonomous underwater geological mapping, mineral concentration analysis, solving equations for mineral composition, a = 2 grams per liter, b = 1.5 grams per liter, oceanic resource mapping, volcanic seabed analysis."]