Solve the following system of equations: 5x + y = 7 y - 8x = -6

To solve the system of equations: $$5x + y = 7$$ $$y - 8x = -6$$ We can use the substitution method. First, let's solve the second equation for y: $$y = 8x - 6$$ Now, substitute this expression for y into the first equation: $$5x + (8x - 6) = 7$$ Combine like terms: $$13x - 6 = 7$$ Add 6 to both sides: $$13x = 13$$ Divide by 13: $$x = 1$$ Now that we have the value of x, we can substitute it back into the equation for y: $$y = 8(1) - 6$$ $$y = 8 - 6$$ $$y = 2$$ So the solution to the system of equations is x = 1 and y = 2. Answer: x = 1, y = 2