To solve this system of equations by graphing, let's examine the equations given:

1. $y = -4x + 2$
2. $y = 5x + 20$

Steps to Solve by Graphing

1. Set the equations equal to each other since both are equal to $y$: $-4x + 2 = 5x + 20$

2. Solve for $x$:

   • Add $4x$ to both sides: $2 = 9x + 20$
   • Subtract $20$ from both sides: $-18 = 9x$
   • Divide by $9$: $x = -2$

3. Substitute $x = -2$ back into one of the equations to find $y$:

   • Using $y = -4x + 2$: $y = -4(-2) + 2$ $y = 8 + 2 = 10$

Solution

The solution to the system is: $(x, y) = (-2, 10)$

Would you like further details on graphing or have any questions?

Here are some related questions to deepen understanding:

1. How do you verify the solution to a system of equations by substitution?
2. What are some advantages of solving systems by graphing versus substitution or elimination?
3. How can we interpret the slopes of these two lines geometrically?
4. What does it mean if two lines are parallel in terms of system solutions?
5. How does changing the intercept of one line affect the solution of the system?

Tip: When graphing linear equations, ensure each line is plotted accurately by using at least two points to define each line, especially when determining intersection points visually.