Determine the number of solutions for the given system. $$ \begin{array}{l}y=6\left(x+\frac{5}{6} ight) \ y=6 x+5 \ ext { One solution } \ ext { No solutions } \ ext { Infinitely many solutions }\end{array} $$

Question

Determine the number of solutions for the given system. $$ \begin{array}{l}y=6\left(x+\frac{5}{6}ight) \ y=6 x+5 \ 	ext { One solution } \ 	ext { No solutions } \ 	ext { Infinitely many solutions }\end{array} $$

UpStudy AI · Accepted Answer

### Step 1
Rewrite the first equation by distributing the constant:
$$
y = 6\left(x + \frac{5}{6}\right) = 6x + 6\left(\frac{5}{6}\right) = 6x + 5.
$$

### Step 2
The system of equations now becomes:
$$
\begin{aligned}
y &= 6x + 5, \
y &= 6x + 5.
\end{aligned}
$$

### Step 3
Since both equations are identical, every solution of one equation will satisfy the other.

### Final Answer
$$
\text{Infinitely many solutions.}
$$
There are infinitely many solutions.

Determine the number of solutions for the given system.

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