To solve the system of linear equations:

$y = 6x - 11$ $-2x - 3y = -7$

Step 1: Substitute $y = 6x - 11$ into the second equation.

Given: $-2x - 3y = -7$

Substitute $y = 6x - 11$: $-2x - 3(6x - 11) = -7$

Step 2: Simplify the equation.

Distribute the $-3$: $-2x - 18x + 33 = -7$

Combine like terms: $-20x + 33 = -7$

Step 3: Solve for $x$.

Subtract 33 from both sides: $-20x = -7 - 33$ $-20x = -40$

Divide both sides by $-20$: $x = 2$

Step 4: Solve for $y$.

Now substitute $x = 2$ back into the first equation: $y = 6(2) - 11$ $y = 12 - 11$ $y = 1$

Solution:

The solution to the system of equations is: $x = 2, \quad y = 1$

Would you like more details or have any questions about this process?

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Here are 5 follow-up questions related to this problem:

1. What is the graphical interpretation of the solution $(2, 1)$ for this system of equations?
2. How would you solve this system using the elimination method?
3. Can you solve the system by converting both equations into slope-intercept form?
4. What would happen if both lines were parallel? How would that affect the solution?
5. How can you verify that $(2, 1)$ is the correct solution?

Tip: When solving systems of equations, always double-check by substituting your solutions back into the original equations to verify accuracy.