Presentation on theme: "Systems of Linear Equations"— Presentation transcript:
1 Systems of Linear Equations DeterminantsGraphs of Parallel Lines Graphs of the Same LineGraphs of IntersectionPractice
2 Determinants What is the use of the determinant? The determinant tells us if there is no solutions/infinitely many or exactly one solution.Given this system of equations, what is the determinant?ax+by=e cx+dy=fThe determinant is a*d – b*c
3 DeterminantsWhat is the determinants of the following systems of linear equations?x= -9 -3x=4-8x+3y=-24 5x+2y=154x-5y=-13 6x-7y=-5
5 Determinants Now what does the determinant number mean? IF the determinant (a*d – b*c) is ZEROTHEN the system of linear equations has no solution or it has infinitely many.This means that the lines are either PARALLEL or they are the SAME line.IF the determinant (a*d – b*c) is NON-ZEROTHEN the system of linear equations has exactly one solution.This means that the two lines intersect!
6 Parallel Lines Parallel lines will have a determinant of ZERO. Take this system of linear equations-6x+3y=9 -12x+6y=-6(-6)*6 – 3*(-12)= 0This system is graphed to the right.
7 Same LineSystems of linear equations that are the same line have a determinant of ZEROTake the system, for example.2x+3y=9 4x+6y=182*6 – 3*4 = 0This system is graphed to the right
8 IntersectionSystems of linear equations that intersect have a determinant that is NON-ZERO.Take this system, for example.4x+6y=-3 6x-2y=24*(-2) – 6*6=-44This system is graphed to the right.
9 Practice: How many solutions? 4x-5y=19 6x+6y=83x+6y=10-2x+4y=38x-3y=22x+7y=915x-5y=255x+20y=474*6 – (-5)*6=543*4 – 6*(-2)=08*7 – (-3)*2=6215*20-(-5)*5=325
10 Practice: How many solutions? 4x-5y=19 6x+6y=83x+6y=10-2x+4y=38x-3y=22x+7y=915x-5y=255x+20y=47No Solutions/Infinitely ManyExactly One Solution