Problem

Solve the system by the substitution method. \[ \begin{aligned} x y & =30 \\ 3 x-y & =-9 \end{aligned} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an ordered pair. Use a comma to separate answers if needed.) B. There is no solution.

Solution

Step 1 :Express y in terms of x from the first equation: \(y = \frac{30}{x}\).

Step 2 :Substitute \(y = \frac{30}{x}\) in the second equation and solve for x.

Step 3 :The solutions for x are -5 and 2.

Step 4 :Substitute x = -5 and x = 2 back into the equation \(y = \frac{30}{x}\) to find the corresponding values of y.

Step 5 :The solutions for y are -6 and 15 when x = -5 and x = 2 respectively.

Step 6 :The solution set is \(\boxed{(-5, -6), (2, 15)}\).

From Solvely APP
Source: https://solvelyapp.com/problems/41133/

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