a)
b)

To solve this system of equations, you can use substitution or elimination. Start with the second equation, . You can express in terms of as . Now, substitute this expression for into the first equation:

This simplifies to , which leads to , so .

Now, plug back into to find :

Therefore, the solution to the system is and , or the point .

In many real-world scenarios, solving systems of equations like this can be applied in economics, chemistry, and engineering, where balancing resources or reactions is essential! For instance, think about mixing different chemicals in a lab; you’ll often have to figure out how to combine substances while respecting their quantities.

Common pitfalls while solving systems include arithmetic errors during multiplication or addition, and forgetting to substitute correctly. Another mistake people often make is overlooking solutions that seem extraneous or don’t fit the original problem context; always verify your answers in both equations!