To solve the system of equations by graphing, let's analyze each equation:

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

   • Rewrite this equation in slope-intercept form (i.e., $y = mx + b$): $y = -x - 2$
   • Here, the slope $m$ is -1, and the y-intercept $b$ is -2.
   • To graph this line, plot the y-intercept (0, -2) and use the slope to find another point. Since the slope is -1, go down 1 unit and right 1 unit from the y-intercept. This gives the point (1, -3).

2. Equation 2: $y = 5x + 4$

   • This is already in slope-intercept form, where the slope $m$ is 5, and the y-intercept $b$ is 4.
   • To graph this line, plot the y-intercept (0, 4) and use the slope to find another point. Since the slope is 5, go up 5 units and right 1 unit. This gives the point (1, 9).

Finding the Intersection

The solution to the system is the point where the two lines intersect.

1. Graph each line based on the points calculated above.
2. Look for the intersection point of the two lines on the graph. After plotting, you'll find that the two lines intersect at the point $(-1, -1)$.

Solution

The solution to the system is: $(x, y) = (-1, -1)$

Would you like more details on the graphing process, or do you have any questions?

Here are some related questions to deepen your understanding:

1. How do you determine the slope and y-intercept of a line?
2. What steps are involved in converting a linear equation to slope-intercept form?
3. How can you verify the solution of a system of equations algebraically?
4. What does the slope represent in a real-world context?
5. How can graphing be used to solve systems of equations with more than two lines?

Tip: When graphing, always check both the slope and y-intercept to ensure accurate plotting.