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Solving Linear Systems by Graphing
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 eqns true.
Ex: Check whether the ordered pairs are solns. of the system
Ex: Check whether the ordered pairs are solns. of the system. x-3y= -5 -2x+3y=10 (-5,0) -5-3(0)= -5 -5 = -5 -2(-5)+3(0)=10 10=10 Solution (1,4) 1-3(4)= -5 1-12= -5 -11 = -5 *doesn’t work in the 1st eqn, no need to check the 2nd. Not a solution.
Solving a System Graphically
Graph each equation on the same coordinate plane. (USE GRAPH PAPER!!!) If the lines intersect: The point (ordered pair) where the lines intersect is the solution. If the lines do not intersect: They are the same line – infinitely many solutions (they have every point in common). They are parallel lines – no solution (they share no common points).
Ex: Solve the system graphically. 2x-2y= -8 2x+2y=4
Ex: Solve the system graphically. 2x+4y=12 x+2y=6
1st eqn: x-int (6,0) y-int (0,3) 2ND eqn: What does this mean? the 2 eqns are for the same line! ¸ many solutions
Ex: Solve graphically: x-y=5 2x-2y=9
1st eqn: x-int (5,0) y-int (0,-5) 2nd eqn: 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!
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