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Transcript
Chapter 2 Lesson 3 Systems of Linear Equations in Two Variables Different methods of solving System of Equations in Two Variables Graphically/Intersection Substitution Elimination Solving a System of Equations Graphically Get both equations into slope-intercept form Y=mx+b Graph Y= menu First equation in Y1 Second equation in Y2 Find both equations on your calculator their intersection 2nd Trace Option 5:intersection Press ENTER 3 times List X and Y values as an ordered pair Examples Solving System of Equations by Substitution In one of the equations, solve for one of the variables Doesn’t matter which one, pick whichever is easier Substitute what that variable equals into the second equation for that variable Has to be other equation, cannot use same equation Solve for the remaining variable Pick an equation to substitute the variable you solved for, solve for the other variable. Doesn’t matter which equation, pick the easier one. Examples Solving a System of Equations by Elimination Multiply one or both of the equations by a constant so that one of the variables has the same coefficient in both equations. If the sign in front of the coefficient is the same in both equations, subtract one equation from the other. If the sign in front of the coefficient is different in both equations, add the equations together. Solve for the remaining variable. In one of the equations, substitute the value in for the variable you solved for, then solve for the remaining variable. Examples Dependent and Inconsistent Systems A system of equations has 3 possible outcomes. 1)The two equations will intersect at one point and have a unique solution. 2)The two equations will graph the same line resulting in an infinite number of solutions, this is called a dependent system. 3)The two equations are parallel and will never intersect, resulting in no solution, this is called an inconsistent system. Examples Homework Page 137-141 1,3,6,9,11,13,15,17,19,21,23,26,31,33,37,38,41,43, 47,49,53,57,63,65