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What causes a solution to a rational equation to be an extraneous solution?

  1. When there is more than one solution, one of the solutions is extraneous.
  2. If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.
  3. If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous.
  4. When a solution is a fraction, the solution is extraneous.

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Hubert Koch
Hubert KochLv2
6 Mar 2020

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30 Sep 2020

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1. Put the following system of equations into an augmented matrix and perform row opera- tions to get the matrix into Row Reduced Echelon Form. Give your answer as r = ..., y = ...,2= .... Marks will be deducted if you leave your solution in matrix form! IF the system is inconsistent, it is sufficient to only Row Reduce, and then clearly state your findings [22 marks]. (a) 2.r + 3y - 2 1 + y +2 y - 22 = = = 4 3 -1 11 +262 +23 ā€“ 3.04 = 2.0 +6.02 + 3.03 - 24 = -X1 + 12 + 2.24 = ri +12 +13 + 3.04 = 1 Ti + 2x2 - 3.13 +224 = -3.01 - 672 +2.13 - 14 = 12 + 2.13 +2 = -Ii - 22 - 2.13 + 4.14 ܝܙ ÜØܝܝ

why is "x āˆ’ y is a rational number" is not antisymmetric while "x = 2y" is antisymmetric

the proof I found for the first one is that "Since (1, āˆ’1) and (āˆ’1, 1) are both in R,
the relation is not antisymmetric." While the proof for the other was, "To see that it is antisymmetric, suppose that x = 2y, and y = 2x. Then y = 4y, from
which it follows that y = 0 and hence x = 0. Thus the only time that (x, y) and (y, x) are both in R
is when x = y (and both are 0)".
now the question is, why is it enough for the first equation to give an example that lies outside the relation to proving that it is NOT antisymmetric. Whereas for the second equation it was enough to give one example to prove that it is antisymmetric, even though in the relation R there exists element which is not antisymmetric

Step 1. Draw an area model for a fraction with units of thirds, fourths, or fifths.

Step 2. Shade in more than one fractional unit.

Step 3. Partition the area model again to find an equal fraction.

Step 4. Write the equivalent fractions as a number sentence. (If you have written a number sentence like this one already in this homework, start over.)

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