6-1 Solving Systems by Graphing Hubarth Algebra

Ex 1 Solving a System of Equation Solve by graphing. Check your solution. y = 2x + 1 y = 3x – 1 Graph both equations on the same coordinate plane. y = 2x + 1 The slope is 2. The y-intercept is 1. y = 3x – 1 The slope is 3. The y-intercept is –1. The lines intersect at (2, 5), so (2, 5) is the solution of the system.

. Ex 2 Solve system by Graphing Solve by Graphing y = 2x – 3 y = x – 1 (2, 1) y = 2x – 3 m = 2 y-int = (0, -3) y = x – 1 m = 1 y-int = (0, -1) The lines intersect at (2, 1), so (2, 1) is the solution of the system.

Ex 3 Systems With No Solution Solve by graphing. y = 3x + 2 y = 3x – 2 Graph both equations on the same coordinate plane. y = 3x – 2 The slope is 3. The y-intercept is –2. y = 3x + 2 The slope is 3. The y-intercept is 2. The two lines have the same slope, different intercepts. The lines are parallel. There is no solution.

Ex 4 Systems With Many Solutions Solve by graphing. 3x + 4y = 12 y = − 3 4 x + 3 Graph both equations on the same coordinate plane. 3x + 4y = 12 The y-intercept is 3. The x-intercept is 4. y = – x + 3 The slope is – . The y-intercept is 3. 3 4 The graphs are the same line. There are many solutions of ordered pairs (x, y), such that y = – x + 3. 3 4

Practice (-1, 5) 1. Solve the system by graphing. y = 2x + 7 y = x + 6 y = 2x + 7 m = 2 y-int= (0, 7) y = x + 6 m = 1 y-int = (0, 6) 2. Solve the system by graphing. y = 4 x = -1 (-1, 4) y = 4 x = -1 3. Solve the system by graphing. y = -2x +1 y = -2x – 3 y = -2x + 1 m = -2 y-int = (0, 1) y = -2x – 3 m = -2 y-int = (0, -3) No solutions, the lines are parallel.