Solve the systems of equations in Exercises 8-11 by...

Solve the systems of equations in Exercises $8-11$ by elimination, and check your solutions. Give the following information:
$\cdot$ which variable you eliminated
$\cdot$ whether you added or subtracted equations
$\bullet$ the solution
$$
\begin{array}{l}{x+y=12} \\ {x-y=6}\end{array}
$$

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Key Concepts

Verification of Solutions

After obtaining a solution to a system of equations, it is important to verify that the solution satisfies all the original equations. This confirmation step ensures that the solution is correct and that no algebraic or arithmetic errors occurred during the problem-solving process.

Elimination Method

The elimination method involves combining equations in a system in such a way that one or more variables are canceled out, making it easier to solve for the remaining variables. This is typically achieved by adding or subtracting equations, based on their coefficients, to eliminate one variable and reduce the system to a single equation.

Systems of Linear Equations

A system of linear equations consists of multiple equations that share common variables. The goal is to find a set of variable values that satisfies all equations simultaneously. This concept is fundamental in algebra and is applicable in various fields including engineering, physics, and economics.

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