To solve the system of equations and , we can use the substitution or elimination method. Adding both equations eliminates :

The solution for the system is .

In real-world applications, systems of equations can represent various scenarios, such as budgeting for a project where resources must be allocated efficiently across competing demands. By finding the intersection of constraints, you can ensure that the project remains feasible!

A common mistake when tackling systems of equations is neglecting to check the solutions back in the original equations. It’s crucial to substitute back in to confirm that the derived values satisfy both equations, ensuring you’ve hit upon the correct solution and not a miscalculation!