Without graphing, is each system independent, dependent, or inconsistent? { - x-3y=0 x-y=4

First, determine if there is a solution to the equation by finding their intersection. If we are to rewrite the system of linear equations,

-x - 3y = 0

x - y = 4

The values of x and y from the equation are 3 and - 1. The slopes of the equations, m, are also not the same as shown below,

m = - A/B

where A and B are the numerical coefficients of x and y, respectively.

m1 = - (-1/-3) = - 1/3

m2 = - (1/-4) = 1/4

Hence, the equations are independent.

Since we can find a solution for this system of equations we can affirm this is an independent system with solution equal to (x, y) = (3,-1)

* If we graph a dependent system in the slope - intercept form, we can see that the graphs of each one are identical to each (beacuse we are representing the same line).

*An inconsistent system occurs when the equations have the same slope, but different values of intersection with the Y axis.