QuestionSolve by the substitution method. $$\begin{array}{l} 2 x+3 y=21 \\ x=15-2 y \end{array}$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set of the system is $\square$ \}. (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. The solution set is the empty set.

Studdy Solution
Verify the solution $(x, y) = (-3, 9)$ by substituting back into the original equations.
First equation:
$$2x + 3y = 21$$
$$2(-3) + 3(9) = 21$$
$$-6 + 27 = 21$$
$$21 = 21$$ (True)
Second equation:
$$x = 15 - 2y$$
$$-3 = 15 - 2(9)$$
$$-3 = 15 - 18$$
$$-3 = -3$$ (True)
Both equations are satisfied, thus the solution is correct.
The solution set of the system is $\{(-3, 9)\}$.