The given system of equations is:

$-6x + y = 16$

$7x + 4y = 2$

Solving for $x$ and $y$:

Step 1: Express $y$ in terms of $x$

From the first equation:

$y = 6x + 16$

Step 2: Substitute into the second equation

$7x + 4(6x + 16) = 2$

$7x + 24x + 64 = 2$

$31x + 64 = 2$

$31x = -62$

$x = -2$

Step 3: Solve for $y$

Substituting $x = -2$ into $y = 6x + 16$:

$y = 6(-2) + 16$

$y = -12 + 16$

$y = 4$

Final Answer:

$\boxed{(-2, 4)}$

Would you like a detailed explanation of any step?

Related Questions:

1. How can we solve this system using the elimination method?
2. What is the determinant of the coefficient matrix in this system?
3. How can we graph these equations and find the solution visually?
4. Can we solve this system using matrices (Gaussian elimination or inverse matrix method)?
5. How does changing the coefficients in the equations affect the solution?

Tip:

When solving a system of equations, always check your solution by substituting back into the original equations to verify correctness.