To solve the system of equations using the graphing method, follow these steps:

Step 1: Rewrite each equation in slope-intercept form (y = mx + b)

1. First equation:
   $-x + y = -5$ Solve for $y$: $y = x - 5$

2. Second equation:
   $2x + y = -2$ Solve for $y$: $y = -2x - 2$

Step 2: Graph the equations

• The first equation $y = x - 5$ has:

  • Slope: $1$ (rise over run: up 1, right 1)
  • y-intercept: $-5$ (point $(0, -5)$)

• The second equation $y = -2x - 2$ has:

  • Slope: $-2$ (rise over run: down 2, right 1)
  • y-intercept: $-2$ (point $(0, -2)$)

Step 3: Find the intersection

• Plot both lines on a graph.
• The intersection point is the solution to the system.

By graphing, you will find that the two lines intersect at $(1, -4)$.

Final Answer:

$\mathbf{(1, -4)}$ This means the solution to the system is $x = 1$, $y = -4$.

Would you like a visual graph or a verification of the solution using substitution?

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Related Questions:

1. How do you verify the solution using substitution?
2. What are alternative methods to solve a system of equations?
3. How do you determine the number of solutions in a system of equations?
4. What happens if two lines are parallel when solving by graphing?
5. Can graphing be inaccurate? When should you use algebraic methods instead?

Tip:

When graphing, use graph paper or a digital tool to get precise intersection points.