Question

how many solutions does the system of equations have? youre trying to find how many solutions this system of equations has. since 3x - 5 would equal y and -5 + 3x would also equal y in the solution to this system, you can set 3x - 5 and -5 + 3x equal to each other to test if there is a solution, or a pair of x - and y - values, that make both equations true at the same time. do that now. the system of equations is \\(\

$$\begin{cases} y = 3x - 5 \\\\ y = -5 + 3x \\end{cases}$$

\\) and there is a coordinate plane with the two lines graphed and a box to fill in \\(\square = \square\\)

Explanation:

Step1: Identify the two expressions for y

We have two equations: \( y = 3x - 5 \) and \( y = -5 + 3x \). Since both equal \( y \), we can set them equal to each other.

Step2: Set the expressions equal

So, \( 3x - 5 = -5 + 3x \).

Answer:

\( 3x - 5 = -5 + 3x \) (After setting the two expressions for \( y \) equal, we can observe that both sides are identical, meaning the system has infinitely many solutions, but for the equation setup as asked, this is the equation.)