b. Solve the system of linear equations using the substitution method. What two numbers did Reese pick?

To solve the system of linear equations using the substitution method, you first need to isolate one variable in one of the equations. Let’s say you have two equations, such as \(x + y = 10\) and \(2x - y = 3\). From the first equation, you could express \(y\) in terms of \(x\) (i.e., \(y = 10 - x\)). Next, substitute this expression for \(y\) into the second equation. You’ll get \(2x - (10 - x) = 3\), which simplifies to \(3x - 10 = 3\). Solving for \(x\), you find \(x = 4.33\), and then plugging it back into the equation \(y = 10 - x\) gives you \(y = 5.67\). So, Reese picked \(x \approx 4.33\) and \(y \approx 5.67\), demonstrating how substitution can lead to solutions in systems of equations! Another fun fact is that substitution isn't just for equations; it's like finding out the secret ingredient in a recipe. Just as you would adjust your substitution to suit your taste in cooking, changing one variable’s value here helps you uncover the delicious numerical combo that satisfies both equations! It's both art and math!