BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION.

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Presentation transcript:

BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION

Using Systems to Solve Equations The graphical method of solving systems of equations can be extended to solving many types of equations. For example:

Graphing is not the only way to solve a system of equations. It is not really the best way because it has to be graphed perfectly and some answers are not integers. SOOOO We need to learn another way!!!!

Solve: by ELIMINATION x + y = 12 -x + 3y = -8

Solve: by ELIMINATION 5x - 4y = x + 4y = 18

Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45

Solve: by ELIMINATION x + y = 30 x + 7y = 6

Solve: by ELIMINATION x + y = 4 2x + 3y = 9 Please take a colored slip and a homework paper as you enter today (on the back table) Then open your notes and solve this problem.

Solve using substitution

Solve using substitution

Types of Solutions Independent solution There is one solution to the system, (2,1) The graphs intersect at one point DependentThere are infinitely many solutions. The graphs are identical/coinciding InconsistentThere are no solutions The lines are parallel