Solve by the elimination method. $$ \begin{array}{r}5 x+6 y=3 \ 10 x+12 y=6\end{array} $$ $$ \begin{array}{r} ext { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \ ext { A. The solution is } \ ext { (Simplify your answer. Type an ordered pair.) } \ ext { B. There are infinitely many solutions. } \ ext { C. There is no solution. }\end{array} $$

Question

Solve by the elimination method. $$ \begin{array}{r}5 x+6 y=3 \ 10 x+12 y=6\end{array} $$ $$ \begin{array}{r}	ext { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \ 	ext { A. The solution is } \ 	ext { (Simplify your answer. Type an ordered pair.) } \ 	ext { B. There are infinitely many solutions. } \ 	ext { C. There is no solution. }\end{array} $$

UpStudy AI · Accepted Answer

We are given the system of linear equations:

$$
5x + 6y = 3
$$

$$
10x + 12y = 6
$$

**Step 1.** Notice that the second equation is exactly twice the first equation:

$$
10x + 12y = 2(5x + 6y) = 2 \times 3 = 6
$$

Since the second equation is a multiple of the first, both equations represent the same line.

**Step 2.** Since the two equations are equivalent, there are infinitely many solutions, as every solution to the first equation is automatically a solution to the second.

**Final Answer:**

B. There are infinitely many solutions.
There are infinitely many solutions.

Solve by the elimination method.

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