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3.1 Solving Linear Systems by Graphing

3.1 Solving Linear Systems by Graphing. p. 139. 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. (1,4) 1-3(4)= -5 1-12= -5 -11 = -5

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3.1 Solving Linear Systems by Graphing

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  1. 3.1 Solving Linear Systems by Graphing p. 139

  2. 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.

  3. (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. (-5,0) -5-3(0)= -5 -5 = -5 -2(-5)+3(0)=10 10=10 Solution Ex: Check whether the ordered pairs are solns. of the system.x-3y= -5-2x+3y=10

  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= -82x+2y=4 (-1,3)

  6. Ex: Solve the system graphically.2x+4y=12x+2y=6 • 1st eqn: x-int (6,0) y-int (0,3) • 2ND eqn: x-int (6,0) y-int (0,3) • 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!

  8. hmwk: 142-143/3-51 mult. of 3

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