7 1 Solving Linear Systems by Graphing Systems

7. 1 Solving Linear Systems by Graphing • Systems of Linear Equations • Solving Systems of Equations by Graphing

Introduction to System of 2 linear equations To solve a linear system by graphing ____ first graph each equation separately. Next identify the intersection _____ of both lines and circle it. That ordered pair is the solution _______ to the system. Check your answer by plugging it system of equations. back into the ______

Solving a System Graphically 1. Graph each equation on the same coordinate plane. (USE GRAPH PAPER!!!) 2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution. 3. If the lines do not intersect: a. They are the same line – infinitely many solutions (they have every point in common). b. They are parallel lines – no solution (they share no common points).

System of 2 linear equations (in 2 variables x & y) • 2 equations with 2 variables (x & y) each. Ax + By = C Dx + Ey = F • Solution of a System – an ordered pair (x, y) that makes both equations true.

Example: Check whether the ordered pairs are solutions of the system. x-3 y= -5 -2 x+3 y=10 A. (1, 4) 1 -3(4)= -5 1 -12= -5 -11 = -5 *doesn’t work in the 1 st equation, no need to check the 2 nd. Not a solution. B. (-5, 0) -5 -3(0)= -5 -5 = -5 -2(-5)+3(0)=10 10=10 Solution

Example: Solve the system graphically. 2 x-2 y= -8 2 x+2 y=4 (-1, 3)

Example: Solve the system graphically. 2 x+4 y=12 x+2 y=6 • 1 st equation: x-int (6, 0) y-int (0, 3) • 2 ND equation: x-int (6, 0) y-int (0, 3) • What does this mean? The 2 equations are for the same line! • many solutions

• Example: Solve graphically: x-y=5 2 x-2 y=9 1 st equation: x-int (5, 0) y-int (0, -5) • 2 nd equation: x-int (9/2, 0) y-int (0, -9/2) • What do you notice about the lines? They are parallel! Go ahead, check the slopes! • No solution!

Assignment: • Complete 6, E, and F on the note taking guide!