17 A store has a certain pair of shoes on sale for dollars and all pairs of socks on sale for dollars. The system of equations shows the total amount spent by customers during the first hour of the sale on two different days.

How many solutions does the system have?
(A) no solution
(B) one solution
© two solutions
(D) infinitely many solutions

Ask by Munoz Gibbs. in Guam

Mar 28,2025

Question

17 A store has a certain pair of shoes on sale for dollars and all pairs of socks on sale for dollars. The system of equations shows the total amount spent by customers during the first hour of the sale on two different days.

How many solutions does the system have?
(A) no solution
(B) one solution
© two solutions
(D) infinitely many solutions

Ask by Munoz Gibbs. in Guam

Mar 28,2025

UpStudy AI · Accepted Answer

We are given the system

$$
\begin{cases}
3x + 2y = 76 \
9x + 6y = 252
\end{cases}
$$

**Step 1.** Notice that multiplying the entire first equation by $$3$$ gives

$$
3(3x + 2y) = 3(76) \quad \Rightarrow \quad 9x + 6y = 228.
$$

**Step 2.** Compare this result with the second equation

$$
9x + 6y = 252.
$$

**Step 3.** Since

$$
228 \neq 252,
$$

the two equations are inconsistent.

**Conclusion:** The system has no solution.

Answer: $$\textbf{(A) no solution}$$.
The system has no solution.