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Graphical Solution of Simultaneous Equations

Learn how to solve simultaneous equations using the graphical method. Plot the equations on a grid and find the point of intersection for the solutions. Examples included.

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Graphical Solution of Simultaneous Equations

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  1. y 10 Solutions x = 7, y = 6 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Solve Example 1 -7 2x – y = 8  -8 x – y = 1 -9 -10 Graphical Solution of Simultaneous Equations Simultaneous Equations can be solved using a graphical method if needed. (7,6) Each equation should be rearranged in the form y = mx +cthen plotted on a grid. The co-ordinates of the point of intersection of each line give the solutions to the equations. y = 2x - 8 y = x - 1

  2. y 10 9 8 Solutions x = 3, y = 7 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Example 2 -7 Solve -8 -9 -2x + y = 1  -10 x + y = 10 Graphical Solution of Simultaneous Equations Simultaneous Equations can be solved using a graphical method if needed. (3,7) Each equation should be rearranged in the form y = mx +cthen plotted on a grid. The co-ordinates of the point of intersection of each line give the solutions to the equations. y = 2x + 1 y = -x + 10

  3. y 10 9 8 Solutions x = 1, y = 4 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 Question -7 Solve -8 -9 -x + y = 3  -10 2x + y = 6 Graphical Solution of Simultaneous Equations Simultaneous Equations can be solved using a graphical method if needed. Each equation should be rearranged in the form y = mx +cthen plotted on a grid. (1,4) The co-ordinates of the point of intersection of each line give the solutions to the equations. y = x + 3 y = -2x + 6

  4. Graphical Solution of Simultaneous Equations y Use the graphs to solve the following simultaneous equations. 10 x + 2y = 14 9 8 7 x – y = 2 1.x - y = 2 and 2x + y = - 8 2x + y = -8 6 5 4 3 2.x + 2y = 14 and y = x + 7 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 3.y = 3x - 10 and x – y = 2 y = x + 7 -2 -3 -4 y = 3x - 10 4.2x + y = - 8 and y = x + 7 -5 -6 -7 -8 5.y = x + 7 and x + 2y = 14 -9 -10 x = -2, y = - 4 x = 0, y = 7 x = 4, y = 2 x = -5, y = 2 x = 0, y = 7

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