Based on the provided image:

Problem:

You need to solve the system of linear equations by using the graphing method. The equations given are:

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

Solution:

1. Graph the Equations:

   • Equation 1: $y = -2x + 1$:
     • Slope ($m$) = -2, y-intercept ($b$) = 1.
     • Plot the y-intercept (0, 1), then use the slope (-2) to plot another point by going down 2 units and right 1 unit.
   • Equation 2: $y = x - 2$:
     • Slope ($m$) = 1, y-intercept ($b$) = -2.
     • Plot the y-intercept (0, -2), then use the slope (1) to plot another point by going up 1 unit and right 1 unit.

2. Find the Intersection:

   • From the graph, the two lines intersect at (1, -1).

3. Verification: Substitute $x = 1$ and $y = -1$ into both equations:

   • $y = -2(1) + 1 = -2 + 1 = -1$ (True for the first equation).
   • $y = 1 - 2 = -1$ (True for the second equation).

Thus, the solution is (1, -1), which corresponds to option D.

Would you like a detailed step-by-step explanation of graphing or anything else clarified?

5 Related Questions:

1. How can you solve a system of linear equations using substitution or elimination methods?
2. What are the differences between graphing and algebraic methods for solving systems of equations?
3. How does the slope-intercept form help in graphing equations quickly?
4. Can all systems of linear equations be solved graphically? What are the limitations?
5. How can technology, like graphing calculators, be used to solve systems of equations?

Tip:

When graphing lines, always double-check the slopes and intercepts to ensure accuracy in locating the intersection point.