Final answer:
The question falls under high school-level mathematics, focusing on the solving of systems of equations and including kinematic equations from physics. Without Joe's specific steps, we address common errors like incorrect substitution, algebraic errors, and selecting inappropriate kinematic equations for solving for a variable in such problems.
Step-by-step explanation:
The subject of the question appears to be mathematics, specifically involving systems of equations and potentially kinematics, given the equations mentioned involve initial and final positions, velocities, accelerations, and time (typically found in physics problems).
Without the actual steps that Joe followed, it's difficult to identify his mistakes, but from the context provided, we can discuss some common errors that can occur when solving for a variable like y or a using substitution and kinematics equations.
Common Mistakes
Incorrectly substituting variables and known values into the equations.
Mathematical errors during algebraic manipulations, such as incorrect sign usage or failing to apply the distributive property properly.
Using the wrong kinematic equation for the given known values and the variable that needs to be solved for.
When using the elimination method to solve simultaneous equations, one must correctly align terms, multiply or divide equations to match coefficients, and then add or subtract the equations to eliminate one of the variables.
In kinematic problems, it involves selecting the appropriate kinematic equation based on the known and unknown quantities and carefully substituting those values to solve for the desired variable.