An Introduction to Graphical Algebra : for the Use of High Schools

Cover An Introduction to Graphical Algebra : for the Use of High Schools
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The two points c, c' have the same value of ;ir = -|- 5, but the corre- sponding y of one is — i and of the other is — 3.
The points a, a! have a common ;tr= — i, but the values J)/ are + 3 and + 5. The points a, b' have the same value j/ = -}- 5, but the values of jr are — i and - 3- This is the geometrical explanation of the fact that when we assume that x and y are alike in (9) and (10) and seek to determine their value by elimination, we find ourselves baffled by the fact that we cannot eli
...mi- nate one without eliminating the other. The equa- tions are both true, but they are not simultaneous.
If in place of equation (10) we take either of the equations •*'+ 27 = 4 (11) 2j? -|- ^ = 8, (12) and combine them with (9), we get in either case the values _j' = o and x = -\- a^. Both of the lines repre- sented by these equations will cross the line represent- ing equation (9) at the point where it crosses the axis X. One of them will cross the axisj/ at a point where y — %, and the other where ^ = 2.


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