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In algebra, an ordered pair typically consists of two numbers used to represent the position of a point on a graph in a coordinate system. The first number is known as the 'x-coordinate' and the second as the 'y-coordinate'. To determine if an ordered pair is a solution to a linear equation, each coordinate is plugged into the equation, replacing the respective variables. For instance, in the equation (-2 x-9 y=7), the ordered pair (-1, -1) represents possible x and y values. If when substituting these into the equation the resulting expression is true, then the pair is a solution. Verification of this forms an essential part of solving linear equations and understanding their graphical representations.

The substitution method is an algebraic technique used to solve systems of equations or to check if an ordered pair satisfies a single equation. This method requires one to replace a variable in an equation with its corresponding value from an ordered pair or another equation. In our case, the ordered pair (-1, -1) is used, replacing 'x' with -1 and 'y' with -1 in the given equation (-2 x-9 y=7). When done properly, if the equation holds true, it confirms the solution. This process of substitution is pivotal as it forms the groundwork for solving more complex systems of equations.

Evaluating expressions is a fundamental process in algebra which involves replacing variables with their values and then performing the indicated operations. Following substitution, in our example, the expression becomes (2 + 9) after applying the necessary mathematical operations. This simplified expression permits us to compute the actual numerical answer, serving as a critical step in gauging the truth of an equation with a given set of variable values. Mastery of evaluation helps students to not only check solutions but also understand how algebraic expressions and equations describe numerical relationships.

To check if an ordered pair is the solution to an equation, we verify that the left and right sides of the equation are equal after we substitute and evaluate the expressions with the pair's values. From our initial example, after substituting (-1, -1) in the equation and evaluating, we arrived at (2 + 9 = 11). Comparison is the final step. We compare our result against the right side of the original equation. If they match, the pair is a valid solution; if not, as in this scenario where 11 does not equal 7, the pair does not satisfy the equation. Checking solutions is integral as it confirms the accuracy of our work and the validity of the potential solutions.