Solve the following system of functions: \(f(x) = 3x + 2\) and \(g(x) = 2x - 1\).
Answer
Finally, we substitute \(x = -3\) into either of the original functions to solve for \(y\). Let's use \(f(x) = 3x + 2\): \(f(-3) = 3(-3) + 2 = -7\). So, the solution to the system of functions is \((-3, -7)\).
Step 1 ：First, we set the two functions equal to each other to solve for \(x\): \(3x + 2 = 2x - 1\).
Step 2 ：Next, we subtract \(2x\) from both sides of the equation: \(x + 2 = -1\).
Step 3 ：Then, we subtract 2 from both sides of the equation: \(x = -3\).
Step 4 ：Finally, we substitute \(x = -3\) into either of the original functions to solve for \(y\). Let's use \(f(x) = 3x + 2\): \(f(-3) = 3(-3) + 2 = -7\). So, the solution to the system of functions is \((-3, -7)\).
