5-5A Determine the Best Method Algebra 1 Glencoe McGraw-HillLinda Stamper

Graphing – can provide a useful method for estimating a solution and to provide a visual model of the problem. Substitution – requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or –1. Elimination Using Addition –convenient when a variable appears in different equations with coefficients that are opposites. Elimination Using Subtraction –convenient if one of the variables has the same coefficient in the two equations. Elimination Using Multiplication –can be applied to create opposites in any system. Ways to Solve a System of Linear Equations

Choose one equation and isolate one of the variables. Solve the linear system using the substitution method. Substitute the expression into the other equation and solve. Substitute the solved value into one of the original equations and solve. Write the answer as an ordered pair. Remember to place the x value first. (–1,0)

Elimination Using Addition Add the equations if one of the variables has opposites. Then solve. Substitute the solved value into either of the original equations to find the value for the other variable. Write the solution as an ordered pair. (4,3) Check by substitution in both original equations.

Elimination Using Subtraction Subtract the equations if one of the variables have the same coefficients. Then solve. Substitute the solved value into either of the original equations to find the value for the other variable. Write the solution as an ordered pair. Check by substitution in both original equations (4,-7)

Elimination Using Subtraction (-1,2) Distribute the negative sign over the entire equation that is subtracted.

Often the equations are not ready for one variable to cancel. You will need to create the opposites. Multiply one or both equations by a number to obtain coefficients that are opposites for one of the variables.

Choose one of the variables to make opposites. Multiply by a number needed to create the opposite. Add your equation because you now have opposites. Write solution as an ordered pair. (–1,2) original Substitute the solved value into either of the original equations to find the value for the other variable.

(-1,2) While you can choose either of the two equations to make opposites, choosing wisely may save you some work. Here is the work if the x variable is used to create the opposite.

When solving a system by elimination, rearrange the terms so that the corresponding variables are vertically stacked. Substitute the solved value into either of the original equations. Write answer as an ordered pair. (0,2)

Solve the linear system. (5,3)

Solve the linear system.

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(20,10)

Solve the linear system.

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5-A7 Pages # 6–16,23-25.