(1) Plot the graphs of the straight lines y = x,  y = 1.1x – 0.2
and y = 0.9x – 0.1

What do the graphs tell you about the solutions to the two pairs of simultaneous equations
y = x
y = 1.1x – 0.2
and
y = x
y = 0.9x – 0.1

(2) Solve the two pairs of simultaneous equations:

x + 0.99999y = 2.99999
0.99999x + y = 2.99998

and
x + 1.00001y = 2.99999
0.99999x + y = 2.99998.

 Explain why the solutions are so different and yet the pairs of equations are nearly identical. Considering the geometrical properties of the lines helps to explain why this happens.
Thanks to NRICH for this problem.

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