$$ 1 \leftarrow \begin{array}{l} ext { Solve the system by the substitution method. } \ \qquad \begin{array}{r}x-2 y=6 \ y\end{array} \ ext { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. }\end{array} $$ OA. The solution set is $$ \} $$. (Type an ordered pair.) OB. There are infinitely many solutions OC. There is no solution.

Question

$$ 1 \leftarrow \begin{array}{l}	ext { Solve the system by the substitution method. } \ \qquad \begin{array}{r}x-2 y=6 \ y\end{array} \ 	ext { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. }\end{array} $$ OA. The solution set is $$ \} $$. (Type an ordered pair.) OB. There are infinitely many solutions OC. There is no solution.

UpStudy AI · Accepted Answer

To solve the system of equations using the substitution method, we first need to express one variable in terms of the other. The given equations are:

1. $$ x - 2y = 6 $$
2. $$ y $$

From the second equation, it seems that $$ y $$ is not defined. However, we can express $$ x $$ in terms of $$ y $$ from the first equation.

Let's solve for $$ x $$ in terms of $$ y $$:

1. Rearranging the first equation gives us:
   $$
   x = 2y + 6
   $$

Now, we can substitute this expression for $$ x $$ back into the second equation. However, since the second equation is just $$ y $$, it does not provide any additional information.

This means we have one equation with two variables, which typically indicates that there are infinitely many solutions. The solutions can be expressed as ordered pairs $$(x, y)$$ where $$ x = 2y + 6 $$.

Thus, the correct choice is:

**OB. There are infinitely many solutions.**
There are infinitely many solutions.

OA. The solution set is . (Type an ordered pair.)
OB. There are infinitely many solutions
OC. There is no solution.

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OA. The solution set is . (Type an ordered pair.) OB. There are infinitely many solutions OC. There is no solution.