(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
y = x
y = 0.9x – 0.1
(2) Solve the two pairs of simultaneous equations:
(2a) x + 0.99999y = 2.99999
0.99999x + y = 2.99998
(2b) x + 1.00001y = 2.99999
0.99999x + y = 2.99998.
Consider the lines with these equations. Explain why the solutions to the equations seem to be different even though the pairs of equations are nearly identical. Does this depend on the scales chosen for the axes?
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This problem is adapted from the NRICH task Intersections with permission of the University of Cambridge. All rights reserved.