 Students will be able to solve linear systems using substitution. In Chapter 3-1, you were able to solve a linear system of equations by rewriting each.

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Presentation transcript:

 Students will be able to solve linear systems using substitution. In Chapter 3-1, you were able to solve a linear system of equations by rewriting each equation in the slope-intercept form. (y = mx + b) By either graphing the equations or evaluating each system’s slope and y-intercept, you were able to determine the number of solutions.

Algebra 2 Foundations, pg Focus Question When can you use substitution to solve a system of linear equations?  Use substitution when one of the equations in the system is already solved for one of the variables. You can use substitution when it is easy to isolate a variable in one of the equations. Sometimes when you solve a system of equations by graphing, you cannot identify the exact coordinates of the point of intersection. You can solve these systems algebraically.  Students will be able to solve linear systems using substitution.

Algebra 2 Foundations, pg 154 To use the substitution method, first isolate one of the variables in one of the equations. Then substitute for that variable in the other equations and solve for the other variable.  Students will be able to solve linear systems using substitution.

Algebra 2 Foundations, pg 157 Focus Question When can you use elimination to solve a system of linear equations?  Use elimination when the system contains a pair of additive inverses. Then add to eliminate a variable.  Students will be able to solve linear systems using elimination.

Algebra 2 Foundations, pg 157  Students will be able to solve linear systems using elimination. You can use the Addition Property of Equality to solve a system of equations. If you add a pair of additive inverses or subtract identical terms, you can eliminate a variable.

 Students will be able to solve linear systems using elimination.

Algebra 2 Foundations, pg 159  Students will be able to solve linear systems using elimination. When you multiply each side of an equation in a system by the same nonzero number, the new system and the original system have the same solutions. The two systems are called equivalent systems. You can use this method to make additive inverses. Focus Question When can you use elimination to solve a system of linear equations?  You can multiply one or both equations by nonzero numbers to make an equivalent system with additive inverses.

Algebra 2 Foundations, pg 158  Students will be able to solve linear systems using elimination.

Algebra 2 Foundations, pg 158  Students will be able to solve linear systems using elimination.

Algebra 2 Foundations, pg 158  Students will be able to solve linear systems using elimination. Solving a system algebraically does not always provide a unique solution. Sometimes you get infinitely many solutions. Sometimes you get no solutions.

 Students will be able to solve linear systems using elimination.