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.
$$
\left\{\begin{array}{c}{-5 x+6 y=-3} \\ {20 x-24 y=12}\end{array}\right.
$$

Key Concepts

Systems of Linear Equations

Systems of linear equations involve finding values for variables that satisfy multiple equations simultaneously. Typically, these systems consist of two or more equations with common variables, and the solution represents the point or set of points where the graphs of the equations intersect. Understanding how to set up and interpret these systems is crucial in algebra and helps in solving real-world problems where multiple conditions must hold true at the same time.

Elimination Method

The elimination method is a widely used technique for solving systems of linear equations. It involves adding or subtracting equations to eliminate one of the variables, thereby reducing the system to an equation with a single unknown. Once one variable is determined, its value can be substituted back into one of the original equations to find the remaining variable. This method streamlines the process of solving simultaneous equations and is particularly effective when the coefficients of one variable are opposites or can be easily made opposites.

Verification of Solutions

Verification of solutions involves substituting the obtained values back into the original equations to confirm that they satisfy all the conditions of the system. This step is essential to ensure accuracy, as it checks for any possible mistakes in the elimination or calculation process. Verifying solutions not only reinforces the correctness of the result but also builds a deeper understanding of the relationships between variables in a system of equations.

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