Graphical method with rearrangement

Graphical method with rearrangement

Secondary 2

6 marks

TGM Original Questions

Consider the equations \(x+y=6\) and \(-2x+3y=8\).

Copy and complete the following tables of values of \(x\) and \(y\) for the equations \(x+y=6\) and \(-2x+3y=8\).[2]
1. For the equation \(x+y=6\):
  \(x\) \(-1\) \(2\) \(5\)
  \(y\)
2. For the equation \(-2x+3y=8\):
  \(x\) \(-1\) \(2\) \(5\)
  \(y\)
On the grid provided below, using the numbered axis scales, draw and label the graphs of \(x+y=6\) and \(-2x+3y=8\) for \(-1\leq x\leq5\).[3]
Hence, solve the simultaneous equations \(x+y=6\) and \(-2x+3y=8\) graphically.[1]

Solution:

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Answer:For \(x=-1,2,5\): first row \(y=7,4,1\); second row \(y=2,4,6\). Intersection \((2,4)\), so \(x=2,y=4\).

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