The uploaded image contains two equations:

1. $y = 3x + 1$
2. $-4x + y = 9$

Solution:

We can solve this system of equations using substitution or elimination. Here, substitution is straightforward because $y$ is already isolated in the first equation.

Step 1: Substitute $y = 3x + 1$ into the second equation:

$-4x + (3x + 1) = 9$

Simplify: $-4x + 3x + 1 = 9$ $-x + 1 = 9$ $-x = 8$ $x = -8$

Step 2: Substitute $x = -8$ back into $y = 3x + 1$:

$y = 3(-8) + 1$ $y = -24 + 1$ $y = -23$

Final Solution:

$x = -8, \, y = -23$

Would you like a detailed explanation of each step?

Here are 5 related questions to deepen understanding:

1. How can we use the elimination method to solve this system of equations?
2. What is the geometric interpretation of this solution?
3. How would the solution change if the second equation were modified to $-4x + y = 10$?
4. How can we check the solution is correct?
5. What happens if we solve this system graphically?

Tip: Always substitute the solution back into the original equations to confirm accuracy!