2 How many solutions does the system $$ \left\{\begin{array}{l}3 x+6 y=18 \ 6 x+12 y=36\end{array} ight. $$ have? (A) 0 (B) 1 (a) 2 (D) Infinite number

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2 How many solutions does the system $$ \left\{\begin{array}{l}3 x+6 y=18 \ 6 x+12 y=36\end{array}ight. $$ have? (A) 0 (B) 1 (a) 2 (D) Infinite number

UpStudy AI · Accepted Answer

We are given the system:
$$
\begin{cases}
3x + 6y = 18 \
6x + 12y = 36
\end{cases}
$$

**Step 1.** Notice that the second equation is exactly twice the first equation:
$$
2(3x+6y)=6x+12y
$$
and
$$
2(18)=36.
$$

**Step 2.** Since the second equation does not provide any new information (it is just a multiple of the first), both equations represent the same line.

**Step 3.** Therefore, there are infinitely many solutions since any $$(x, y)$$ that satisfies the first equation will also satisfy the second.

The correct answer is:

(D) Infinite number.
There are infinitely many solutions.

2 How many solutions does the system \( \left\{\begin{array}{l}3 x+6 y=18 \\ 6 x+12 y=36\end{array}\right. \) have? (A) 0 (B) 1 (a) 2 (D) Infinite number

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