Substitute the third equation into the second:
Then , and the first equation becomes
With the system is
From :, so . Then , so ,, and .
Example 1.1.
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Idea: choose , so that only has one variable.
Or substitute: from the first equation , so
So the power of in is , i.e. and . Then
and indeed . So ,.
Problem 1.31. Win ratio . At the start of the weekend . Over the weekend: matches, won and lost. At the end, . What is the largest number of matches won before the weekend began?
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, and
1.1 Isolation
Problem 1.1. (a)
(b)
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(a) .
(b) .
Problem 1.2. (a)
(b)
(c)
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(a) .
(b) .
(c) .
Problem 1.3. Compute and solve: .
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.
Problem 1.4. Compute and solve:
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Moving the first fraction across, , so
Problem 1.5. Find all such that
has no solution for .
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No solution is when , i.e. .
Also causes division by in the original equation. So set
no solution, so there are no values of for which . Note is also not a solution.
So and are the two values which give no solution.
Exercises
Exercise 1.1.4. Find all such that has no solution for .