The given system of equations is:

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

We can solve this system of equations using substitution. Since the second equation is already solved for $y$, substitute $y = 7x - 6$ into the first equation:

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

Simplify:

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

Solve for $x$:

$3x = 12$ $x = 4$

Find $y$:

Substitute $x = 4$ into $y = 7x - 6$: $y = 7(4) - 6$ $y = 28 - 6$ $y = 22$

Solution:

The solution to the system of equations is: $x = 4, \, y = 22$

Would you like a step-by-step explanation of the method, or have any questions?

Related Questions:

1. How can we verify the solution of this system of equations?
2. What is the graphical interpretation of this solution?
3. How do we solve systems of equations with elimination instead of substitution?
4. What happens when two lines have no solution (parallel)?
5. What is the effect of altering the coefficients in the equations?

Tip:

Always check your solution by substituting both values back into the original equations to ensure accuracy.