Solving a System by Elimination In Exercises 13-30, solve...

Solving a System by Elimination In Exercises
$13-30,$ solve the system by the method of elimination and
check any solutions algebraically.
$$
\left\{\begin{array}{l}{3 x+2 y=10} \\ {2 x+5 y=3}\end{array}\right.
$$

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Key Concepts

System of Linear Equations

This concept involves a set of equations containing the same variables, where each equation represents a line (or hyperplane in higher dimensions). The objective is to find values for the variables that satisfy all equations simultaneously, typically corresponding to their point of intersection.

Elimination Method

The elimination method is a systematic approach used to solve systems of equations by strategically adding or subtracting equations to cancel out one of the variables. Often, this process involves multiplying one or more equations by constants so that the coefficients of one of the variables match, allowing for its elimination and ultimately reducing the system to a single equation with one variable.

Algebraic Verification

After obtaining a solution through elimination, it is important to substitute the values back into the original equations to verify that they satisfy all the equations. This algebraic check ensures the accuracy of the solution and confirms that no errors were made during the process.

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