In the following exercises, determine if the following...

In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
-3 x+y=8 \\
-x+2 y=-9
\end{array}\right.
$$
(a) (-5,-7) (b) (-5,7)

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Key Concepts

Substitution Method for Verification

The substitution method for verification involves plugging the values of the variables from the candidate solution into each equation of the system. If after substitution, each equation holds true (i.e., both sides of the equation are equal), then the candidate solution is confirmed to be valid.

Solution Verification

Solution verification is the process of checking if a proposed solution actually satisfies all the equations in the system. This involves substituting the values from the candidate solution into each equation and confirming that the resulting statements are true.

Ordered Pair Representation

In a two-variable system, solutions are typically expressed as ordered pairs. This ordered pair indicates specific values for the variables (usually x and y) that, when substituted into each equation of the system, satisfy every equation at the same time.

System of Linear Equations

A system of linear equations is a set of two or more equations that involve the same set of variables. The goal when dealing with such systems is to find the value(s) of the variable(s) that satisfy all equations simultaneously, which represents the point or points of intersection of the lines represented by the equations.

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