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7.1 Solving Linear Systems by Graphing

Learn how to solve systems of linear equations by graphing them on a coordinate plane, identifying intersection points, and checking solutions in this introduction to solving linear systems graphically.

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7.1 Solving Linear Systems by Graphing

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  1. 7.1 Solving Linear Systems by Graphing Systems of Linear Equations Solving Systems of Equations by Graphing

  2. Introduction to System of 2 linear equations 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

  3. 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).

  4. 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.

  5. Example: Check whether the ordered pairs are solutions of the system.x-3y= -5-2x+3y=10 • (1,4) 1-3(4)= -5 1-12= -5 -11 = -5 *doesn’t work in the 1st equation, 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

  6. Example: Solve the system graphically.2x-2y= -82x+2y=4 (-1,3)

  7. Example: Solve the system graphically.2x+4y=12x+2y=6 • 1st equation: x-int (6,0) y-int (0,3) • 2ND equation: x-int (6,0) y-int (0,3) • What does this mean? The 2 equations are for the same line! • many solutions

  8. Example: Solve graphically: x-y=5 2x-2y=9 • 1st equation: x-int (5,0) y-int (0,-5) • 2nd 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!

  9. Assignment: • Complete 6, E, and F on the note taking guide!

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