1. Stating the problem: Solve the system of linear equations: $$-6x + 2y = 16$$ $$-7x + 6y = 26$$ 2. We will use the method of elimination to solve for $x$ and $y$. 3. Multiply the first equation by 3 to align the coefficients of $y$: $$3(-6x + 2y) = 3(16)$$ $$-18x + 6y = 48$$ 4. Now subtract the second equation from this new equation: $$(-18x + 6y) - (-7x + 6y) = 48 - 26$$ 5. Simplify the left side by canceling $6y$: $$-18x + 6y + 7x - 6y = 22$$ $$(-18x + \cancel{6y}) + (7x - \cancel{6y}) = 22$$ $$-18x + 7x = 22$$ 6. Combine like terms: $$-11x = 22$$ 7. Solve for $x$ by dividing both sides by $-11$: $$x = \frac{22}{-11}$$ $$x = -2$$ 8. Substitute $x = -2$ into the first original equation to solve for $y$: $$-6(-2) + 2y = 16$$ $$12 + 2y = 16$$ 9. Subtract 12 from both sides: $$2y = 16 - 12$$ $$2y = 4$$ 10. Divide both sides by 2: $$y = \frac{4}{2}$$ $$y = 2$$ Final answer: $$x = -2, y = 2$$