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

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Key Concepts

Coefficient Multiplication

Coefficient multiplication is a technique used in the elimination method where each equation in the system is multiplied by a suitable constant. This is done to create equal or opposite coefficients for one of the variables in different equations, thereby facilitating the cancellation of that variable when the equations are added or subtracted.

Elimination (Addition) Method

The elimination method, also known as the addition method, is a procedure to solve systems of linear equations by adding or subtracting the equations to cancel out one of the variables. This process involves modifying one or both of the equations, so their coefficients align in a way that one variable is eliminated, making it simpler to solve for the remaining variable.

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same set of variables. These equations are studied simultaneously because their solution is the set of variable values that satisfy every equation in the system. They form the basis for techniques used in areas such as algebra, engineering, and economics for modeling and solving real-world problems.

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