(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
(1a) y = x
y = 1.1x – 0.2
and
(1b) 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
and
(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?
Click here to download the INTERSECTIONS worksheet.
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This problem is adapted from the NRICH task Intersections with permission of the University of Cambridge. All rights reserved.
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