7.1 Solving Linear Systems by Graphing Systems of Linear Equations Solving Systems of Equations by Graphing

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

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-3y= -5 -2x+3y=10 A.(1,4) 1-3(4)= = = -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 -2(-5)+3(0)=10 10=10 Solution

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

Example : Solve the system graphically. 2x+4y=12 x+2y=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 2x-2y=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!