Question

graph the system on a separate sheet of paper and determine the number of solutions it has. if it has one solution, determine its coordinates.
y = -3
y = x - 3

a) 1 solution; (0, -3)
b) infinitely many solutions
c) 1 solution; (3, 0)
d) no solution

Explanation:

Step1: Substitute \( y = -3 \) into the second equation

We have the system \(

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

\). Substitute \( y=-3 \) into \( y=x - 3 \), we get \( -3=x - 3 \).

Step2: Solve for \( x \)

Add 3 to both sides of the equation \( -3=x - 3 \). So \( -3 + 3=x-3 + 3 \), which simplifies to \( 0=x \), or \( x = 0 \).

Step3: Determine the solution

Since \( x = 0 \) and \( y=-3 \), the solution of the system is \( (0,-3) \), and there is 1 solution.

Answer:

A) 1 solution; \( (0, -3) \)