Evaluate x^2 - (xy - y) for x satisfying 3(x + 3)/5 = 2x + 6 and y satisfying - 2y - 10 = 5y + 18.

Key Concepts

Solving Linear Equations

To evaluate the expression, we first need to solve the linear equations for x and y. A linear equation is an equation of the first degree, meaning it can be written in the form ax + b = 0. We isolate the variable by performing inverse operations, allowing us to find the specific values of x and y needed for the evaluation.

Substitution

Once we have the values of x and y, we use substitution to evaluate the expression x^2 - (xy - y). Substitution involves replacing variables in an expression with their corresponding values. This step is crucial as it allows us to compute the final result by simplifying the expression with the known values.

Polynomial Evaluation

The expression x^2 - (xy - y) is a polynomial, and evaluating it involves performing arithmetic operations on the variables. A polynomial is a mathematical expression consisting of variables raised to whole number powers. Understanding how to manipulate and simplify polynomials is essential for accurately calculating the final value after substitution.