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.
$$
\left\{\begin{aligned} x+5 y &=10 \\ 3 x-10 y &=-5 \end{aligned}\right.
$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. This concept is fundamental in algebra and is applied in various fields of science and engineering.

Elimination Method

The elimination method is a technique for solving systems of equations by strategically adding or subtracting equations to eliminate one of the variables. This is done by obtaining equal coefficients for one of the variables in the equations, making it possible to cancel that variable out. The remaining equation can then be solved for the other variable, and its value is substituted back into one of the original equations to find the eliminated variable.

Algebraic Verification

Algebraic verification involves substituting the obtained solution back into the original equations to ensure that each equation is satisfied. This step is important because it confirms the correctness of the solution and rules out any possible computational errors. It is a common and essential practice to validate the results after solving a system of equations manually.

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