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Maths

Simultaneous equations - Higher

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Solving simultaneous equations using graphs

Solving simultaneous equations using a graph is easier than you might think. First, you need to draw the lines of the equations. The points where the lines cross is the solution.

Linear equations

The graphs of linear equations will give straight lines.

Example

  • Solve these simultaneous equations by drawing graphs:
  • 2x + 3y = 6
  • 4x - 6y = - 4

For example, to draw the line 2x + 3y = 6 pick two easy numbers to plot. One when x = 0 and one where y= 0

  • When x = 0 in the equation 2x + 3y = 6
  • This means 3y = 6 so y = 2
  • So one point on the line is (0, 2)
  • When y = 0
  • 2x = 6 so x = 3
  • So another point on the line is (3 ,0)

In an exam, only use this method if you are prompted to by a question. It is usually quicker to use algebra if you are not asked to use graphs.

image: graph showing 2x + 3y = 6 and 4x minus 6y = minus 4

Linear and quadratic equation

Example

  • Solve the simultaneous equations by drawing graphs.
  • y - 2x = 1
  • y = x2 - 2
image: graph showing y minus 2x = 1 and y = x to the power of 2 minus 2

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