Question

solve the system by graphing.\

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

use the graphing tool to graph the system.

Explanation:

Step1: Analyze the second equation

The equation \( y = 3 \) is a horizontal line where all points have a \( y \)-coordinate of 3. To graph it, we can plot points like \( (0, 3) \), \( (1, 3) \), \( (2, 3) \), etc., and draw a horizontal line through them.

Step2: Rewrite the first equation

Rewrite \( x - y = 1 \) in slope - intercept form (\( y=mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept). Solve for \( y \):
\( x - y=1\) can be rewritten as \( y=x - 1 \). The slope \( m = 1 \) and the \( y \)-intercept \( b=- 1 \). To graph this line, we can start at the \( y \)-intercept \( (0,-1) \) and use the slope (rise 1, run 1) to find other points, such as \( (1,0) \), \( (2,1) \), etc.

Step3: Find the intersection point

The solution to the system of equations is the point where the two lines \( y = 3 \) and \( y=x - 1 \) intersect. Substitute \( y = 3 \) into the equation \( y=x - 1 \):
\( 3=x - 1 \)
Add 1 to both sides of the equation:
\( x=3 + 1=4 \)
So the intersection point is \( (4,3) \).

Answer:

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