Question

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\ ight. $$

Explanation:

Step1: Analyze the system of equations

The given system is \(

$$\begin{cases}y = 2\\y=2\end{cases}$$

\). This is a system of two identical linear equations. In a coordinate plane, the equation \(y = c\) (where \(c\) is a constant) represents a horizontal line passing through the point \((x,c)\) for all real - valued \(x\).

Step2: Determine the solution set

Since both equations are \(y = 2\), every point \((x,2)\) where \(x\in R\) (the set of all real numbers) satisfies both equations. Geometrically, the two lines (which are actually the same line) overlap completely.

Answer:

The system of equations \(

$$\begin{cases}y = 2\\y = 2\end{cases}$$

\) has infinitely many solutions. The solution set is \(\{(x,2)|x\in R\}\), which means all points on the horizontal line \(y = 2\) are solutions.