6 1 Solving Systems by Graphing Hubarth Algebra

6 -1 Solving Systems by Graphing Hubarth Algebra

Ex 1 Solving a System of Equation Solve by graphing. Check your solution. y = 2 x + 1 y = 3 x – 1 Graph both equations on the same coordinate plane. y = 2 x + 1 The slope is 2. The y-intercept is 1. y = 3 x – 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 = 2 x – 3 y=x– 1 y = 2 x – 3 m=2 y-int = (0, -3) y=x– 1 m=1 y-int = (0, -1) . (2, 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 = 3 x + 2 y = 3 x – 2 Graph both equations on the same coordinate plane. y = 3 x + 2 The slope is 3. The y-intercept is 2. y = 3 x – 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 Graph both equations on the same coordinate plane. 3 x + 4 y = 12 The y-intercept is 3. The x-intercept is 4. y = – 3 x + 3 The slope is – 3. The y-intercept is 3. 4 4 The graphs are the same line. There are many solutions of ordered pairs (x, y), such that y = – 3 x + 3. 4

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