https://file.aiquickdraw.com/mathbot/file/1727376238920yoor7s4a.jpg

The system of equations given in the image is:

1. \( y = 2x - 5 \)
2. \( y = -x + 1 \)

You are asked to solve this system graphically. To do this, let's find the points where the two lines intersect.

### Step 1: Graph the first equation \( y = 2x - 5 \)
This is a straight line with:
- Slope \( m = 2 \) (meaning it rises 2 units for every 1 unit increase in \( x \)).
- Y-intercept at \( (0, -5) \).

You can plot this line by starting at \( (0, -5) \) and using the slope to move up 2 units and 1 unit to the right to plot additional points.

### Step 2: Graph the second equation \( y = -x + 1 \)
This is also a straight line with:
- Slope \( m = -1 \) (meaning it falls 1 unit for every 1 unit increase in \( x \)).
- Y-intercept at \( (0, 1) \).

Plot this line starting at \( (0, 1) \) and moving down 1 unit and 1 unit to the right to mark more points.

### Step 3: Find the Intersection Point
The intersection of these two lines gives the solution to the system of equations. Solving algebraically:

Set \( 2x - 5 = -x + 1 \).

\[
2x + x = 1 + 5
\]
\[
3x = 6 \quad \Rightarrow \quad x = 2
\]

Substitute \( x = 2 \) into one of the original equations, say \( y = 2x - 5 \):

\[
y = 2(2) - 5 = 4 - 5 = -1
\]

Thus, the solution is \( x = 2 \), \( y = -1 \). The lines intersect at the point \( (2, -1) \).

Do you want more details or have any further questions? Here are some related questions to deepen your understanding:

1. How can you verify if the solution \( (2, -1) \) satisfies both equations?
2. What happens if two lines are parallel in a system of equations? How is the solution affected?
3. Can you solve this system using substitution or elimination, and how does the solution compare?
4. What does the slope of a line tell you about how it behaves on a graph?
5. How would the graph look if the lines were perpendicular?

**Tip**: When graphing lines, always pay attention to the slope and y-intercept, as they determine the position and steepness of the line.

Solve the system of equations graphically: y = 2x - 5 and y = -x + 1.

Learn how to graphically solve the system of linear equations y = 2x - 5 and y = -x + 1. This tutorial covers key algebraic concepts like graphing lines and finding their intersection, suitable for students in Grades 8-10.

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