2 System of 2 linear equations (in 2 variables x & y) 2 equations with 2 variables (x & y) each.Ax + By = CDx + Ey = FSolution of a System –an ordered pair (x,y) that makes both eqns true.
3 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)=1010=10Solution(1,4)1-3(4)= -51-12= -5-11 = -5*doesn’t work in the 1st eqn, no need to check the 2nd.Not a solution.
4 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).
5 Ex: Solve the system graphically. 2x-2y= -8 2x+2y=4 (-1,3)
6 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
7 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!