Solve each system of equations using the addition method. 7...

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The goal is to find a set of values for the variables that satisfies every equation simultaneously. This concept is fundamental in algebra and is widely used in various fields including engineering, economics, and physics.

Elimination (Addition) Method

The elimination method, also known as the addition method, is a technique for solving systems of linear equations. It involves adding or subtracting the equations, often after multiplying them by suitable numbers, to cancel one of the variables. This reduces the system to a single equation with one variable, which can then be solved easily before back-substituting to find the remaining variable.

Coefficient Manipulation

Coefficient manipulation is the process of multiplying one or both equations by appropriate constants to align the coefficients of one of the variables. This alignment allows for the elimination of that variable when the equations are added or subtracted. This step is crucial when the equations do not initially have coefficients that easily allow for elimination.

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