Solving a System of Equations in Two Variables By Graphing Chapter 8.1.

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Presentation transcript:

Solving a System of Equations in Two Variables By Graphing Chapter 8.1

When graphing two equations there are 3 possible scenarios. 1. The two lines could intersect at 1 unique point. (-2, 4)

When graphing two equations there are 3 possible scenarios. 2. The two lines could be parallel and never intersect. Inconsistent system of equations No Solution

When graphing two equations there are 3 possible scenarios. 3. The two lines could be the same line (coincide). Dependent equations Infinite number of solutions

Graphing a system of equations 1. May have to rewrite each equation into y = mx + b. 2. Plot the points and draw each line. 3. Determine the solution.

y = mx + b x + y = 12 y = -x x -x m = - 1, b = 12 -x + y = 4 +x +x y = x + 4 m = 1, b = 4 1. Solve by graphing.

m = - 1, b = 12 m = 1, b = 4 (4, 8) x + y = 12 -x + y = 4 x + y = 12 -x + y = 4 1. Solve by graphing. lines intersect

y = mx + b 4x + 2y = 8 2y = -4x x -4x y = -2x + 4 m = -2, b = 4 -6x – 3y = 6 -3y = 6x x +6x y = -2x – 2 m = -2, b = Solve by graphing.

x m = - 2, b = 4 m = -2, b = -2 4x + 2y = 8 -6x – 3y = 6 4x + 2y = 8 -6x – 3y = 6 No Solution Inconsistent system of equations 2. Solve by graphing. parallel lines

y = mx + b 3x – 9y = 18 -9y = -3x x -3x y =  x – 2 m = , b = -2 -4x + 12y = y = 4x – 24 +4x +4x y =  x – 2 m = , b = Solve by graphing.

m = , b = -2 m = , b = -2 3x – 9y = 18 -4x + 12y = -24 Infinite number of solutions Dependent equations 3x – 9y = 18 -4x + 12y = Solve by graphing. lines coincide

Solving a System of Equations in Two Variables By Graphing Chapter 8.1