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 \(-2x+3y=8\).
For the equation \(x+y=6\):
\(x\)
\(-1\)
\(2\)
\(5\)
\(y\)
For the equation \(-2x+3y=8\):
\(x\)
\(-1\)
\(2\)
\(5\)
\(y\)
On the grid provided below, using a scale of 1 cm to represent 1 unit on both axes, draw and label the graphs of \(x+y=6\) and \(-2x+3y=8\) for \(-1\leq x\leq5\).
Hence, solve the simultaneous equations \(x+y=6\) and \(-2x+3y=8\) graphically.
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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 \(x=2,y=4\).