To solve the system of linear equations using substitution, we are given:

$3x + y = -9 \quad (1)$ $y = 5x + 7 \quad (2)$

Steps:

1. Substitute equation (2) into equation (1): Since $y = 5x + 7$, replace $y$ in equation (1) with $5x + 7$: $3x + (5x + 7) = -9$

2. Simplify the equation: $3x + 5x + 7 = -9$ $8x + 7 = -9$

3. Solve for $x$: Subtract 7 from both sides: $8x = -9 - 7$ $8x = -16$ Divide by 8: $x = -2$

4. Substitute $x = -2$ into equation (2) to find $y$: $y = 5(-2) + 7$ $y = -10 + 7$ $y = -3$

Solution:

The solution to the system of equations is $x = -2$ and $y = -3$. Therefore, the solution is $(-2, -3)$.

Would you like further clarification or additional details?

Here are five related questions to expand on this topic:

1. How do you solve a system of equations using elimination instead of substitution?
2. What are the conditions for a system of linear equations to have no solution?
3. How can graphing be used to solve a system of linear equations?
4. What is the difference between dependent and independent systems of equations?
5. How do you verify if a solution to a system of equations is correct?

Tip: Always double-check your substitution to ensure accuracy when solving systems of equations.