Question

solve the system by graphing.\

$$\begin{cases}x - y = 1\\\\y = 3\\end{cases}$$

\dots\use the graphing tool to graph the system.\click to enlarge graph

Explanation:

Step1: Analyze the second equation

The equation \( y = 3 \) is a horizontal line where all points have a \( y \)-coordinate of 3.

Step2: Rewrite the first equation

Rewrite \( x - y = 1 \) in slope - intercept form (\( y=mx + b \)). Solve for \( y \):
\( y=x - 1 \)
The slope \( m = 1 \) and the \( y \)-intercept \( b=- 1 \).

Step3: Find the intersection point

We know that \( y = 3 \). Substitute \( y = 3 \) into the first equation \( x-y=1 \):
\( x - 3=1 \)
Add 3 to both sides of the equation:
\( x=1 + 3=4 \)

Answer:

The solution to the system of equations is \( x = 4,y = 3 \), or the ordered pair \( (4,3) \).