For choice A, we can rearrange the equation to so it has exactly one solution,
For choice B, we rearrange the equation to so this too has exactly one solution,
Rearranging the equation in choice C by eliminating the terms gives us the false equality
so this equation has no solutions.
Eliminating in the equation in choice D gives the equality
which is always true, so this equation has infinitely many solutions.
Thus, we conclude that choices A and B work.
The top smaller sub-triangle and the whole big triangle are similar. This means that the correspondant sides are in proportion. So, we have
Which implies
So, we have
Answer:
(x, y) = (1/2, -1)
Step-by-step explanation:
Subtracting twice the first equation from the second gives ...
(2/x +1/y) -2(1/x -5/y) = (3) -2(7)
11/y = -11 . . . . simplify
y = -1 . . . . . . . multiply by y/-11
Using the second equation, we can find x:
2/x +1/-1 = 3
2/x = 4 . . . . . . . add 1
x = 1/2 . . . . . . . multiply by x/4
The solution is (x, y) = (1/2, -1).
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<em>Additional comment</em>
If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.
A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).
