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Graphical Method for Solving Simultaneous Equations

Learn how to find values that satisfy two equations by graphing them, discovering the unique pair satisfying both equations. Practice examples and solutions included.

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Graphical Method for Solving Simultaneous Equations

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  1. Solving Simultaneous Equations Finding values which will fit into two equations, using a graph

  2. Think about these two equations Today we will find out what that coordinate using graphs y + x =7 2x – y=-1 There are an infinite number of x and y values which would work here But only 1 pair of numbers which work with both (1,3) (2,5) (4,9) (6,1) ? (3,4) (0,1) (7,0) (5,11)

  3. Example Solve the simultaneous equations x + y=7 and 2x-y=-1 graphically

  4. On the same axis • Cover the y with your finger, it now says x=7, mark 7 on the x axis • Now cover the x, it now says y=7 mark 7 on the y axis • Connect the points • Done x + y =7

  5. The cover up method • Cover the y with your finger, it now says 2x=-1, so x=-0.5, mark this on the x axis • Now cover the x, it now says –y=-1 so y=1, mark this on the y axis • Connect the points • Done 2x - y =-1

  6. 7 (2,5) 1 -0.5 7

  7. Example Solve the simultaneous equations 4x+y=16 and 2x + y=12 graphically

  8. The cover up method • Cover the y with your finger, it now says 4x=16, so x=4, mark this on the x axis • Now cover the x, it now says y=16, mark this on the y axis • Connect the points • Done 4x + y =16

  9. On the same axis • Cover the y with your finger, it now says 2x=12, so x=6 mark 6 on the x axis • Now cover the x, it now says y=12 mark 12 on the y axis • Connect the points • Done 2x + y =12

  10. 16 12 (2,8) 4 6

  11. Questions Solve these simultaneous equations: • 2x+3y=24 and x + 2y=14 • x + y =8 and x + 2y=14 • 3x + 2y=18 and 3x + 4y=24 • 2x + y =11 and 3x-2y=6 • x + y =6 and 2x + y =10 • x +y=5 and 3x+y=9 Answers • (6,4) • (2,6) • (4,3) • (4,3) • (4,2) • (2,3)

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