Answer: To classify the system of equations, we need to compare the slopes and y-intercepts of the two equations. If the slopes are different, then the system is independent and has one solution. If the slopes are equal and the y-intercepts are different, then the system is inconsistent and has no solution. If the slopes and y-intercepts are both equal, then the system is dependent and has infinitely many solutions.
To find the slope and y-intercept of an equation, we can rewrite it in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
The first equation is x - 3y = 5. To rewrite it in slope-intercept form, we can subtract x from both sides and then divide by -3:
x - 3y = 5 -3y = -x + 5 y = (1/3)x - (5/3)
The slope of this equation is 1/3 and the y-intercept is -5/3.
The second equation is 2x + y = 6. To rewrite it in slope-intercept form, we can subtract 2x from both sides and then divide by 1:
2x + y = 6 y = -2x + 6
The slope of this equation is -2 and the y-intercept is 6.
Since the slopes are different, we can conclude that the system is independent and has one solution. This means that the two lines intersect at one point, which is the solution of the system.