To solve the system of linear equations:

1. $y = -6x - 7$
2. $4x - y = -3$

we can use either substitution or elimination. Let's use the substitution method since $y$ is already expressed in terms of $x$ in the first equation.

Step 1: Substitute $y$ in the Second Equation

Given $y = -6x - 7$, substitute this value into the second equation:

$4x - (-6x - 7) = -3$

Simplify:

$4x + 6x + 7 = -3$

$10x + 7 = -3$

Step 2: Solve for $x$

Subtract 7 from both sides:

$10x = -3 - 7$

$10x = -10$

Divide by 10:

$x = -1$

Step 3: Solve for $y$

Substitute $x = -1$ back into the first equation:

$y = -6(-1) - 7$

$y = 6 - 7$

$y = -1$

Solution

The solution to the system of equations is:

$x = -1, \quad y = -1$

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

Here are 5 related questions to consider:

1. How can you solve a system of equations using the elimination method?
2. What is the graphical interpretation of solving a system of linear equations?
3. How do you solve systems of equations that are nonlinear?
4. What are the conditions for a system of equations to have no solution or infinitely many solutions?
5. How can matrices be used to solve systems of linear equations?

Tip: When dealing with systems of equations, always check your solution by substituting the values back into the original equations to verify they are correct.