Solve the system of equations: $$7x + 3y = 1$$ $$2x - 6y = -10$$

Solution:

We can solve this system of equations using the elimination method.

1. Multiply the first equation by 2 to make the coefficients of y opposites: $$2(7x + 3y) = 2(1) ightarrow 14x + 6y = 2$$
2. Add the modified first equation to the second equation: $$(14x + 6y) + (2x - 6y) = 2 + (-10)$$ $$16x = -8$$
3. Solve for x: $$x = \frac{-8}{16} = -\frac{1}{2}$$
4. Substitute the value of x back into the first equation: $$7(-\frac{1}{2}) + 3y = 1$$ $$-\frac{7}{2} + 3y = 1$$ $$3y = 1 + \frac{7}{2}$$ $$3y = \frac{2}{2} + \frac{7}{2}$$ $$3y = \frac{9}{2}$$ $$y = \frac{9}{2} \div 3$$ $$y = \frac{9}{2} \cdot \frac{1}{3}$$ $$y = \frac{3}{2}$$

Answer: $$x=-\frac{1}{2}, y=\frac{3}{2}$$