To solve the system of equations by graphing, follow these simple steps:

The system of equations is:

1. $y = x - 3$
2. $y = -x + 5$

Step 1: Graph $y = x - 3$

• Slope: $1$ (up 1, right 1).
• Y-intercept: $-3$ (this is where the line crosses the y-axis).

1. Plot the point $(0, -3)$ on the graph.
2. From $(0, -3)$, move up 1 unit and right 1 unit to get another point $(1, -2)$.
3. Draw a straight line through these points.

Step 2: Graph $y = -x + 5$

• Slope: $-1$ (down 1, right 1).
• Y-intercept: $5$ (this is where the line crosses the y-axis).

1. Plot the point $(0, 5)$ on the graph.
2. From $(0, 5)$, move down 1 unit and right 1 unit to get another point $(1, 4)$.
3. Draw a straight line through these points.

Step 3: Find the Intersection

• The solution to the system of equations is where the two lines intersect.
• By looking at the graph, the lines intersect at $(4, 1)$.

Final Answer:

$x = 4$ and $y = 1$.

Let me know if you need help graphing or a clearer explanation!

Related Questions:

1. How do you check if the solution $(4, 1)$ satisfies both equations?
2. What is the slope-intercept form of a line?
3. How do you find the slope of a line from two points?
4. How can you graph a line if you're only given the slope and y-intercept?
5. What happens if two lines don't intersect (parallel lines)?

Tip:

Always check your solution by plugging the intersection point back into both equations!