Final answer:
The system of linear equations -x-2y=7 and 5x-y=2 is independent.
Step-by-step explanation:
To determine whether the system of linear equations -x-2y=7 and 5x-y=2 is independent, dependent, or inconsistent without graphing, we can use the method of elimination.
First, we can multiply the second equation by 2 to make the coefficients of y match:
10x-2y=4
Next, we can add the two equations together:
(-x-2y) + (10x-2y) = 7 + 4
This simplifies to:
9x = 11
To isolate x, we divide both sides of the equation by 9:
x = 11/9
Substituting this value of x back into one of the original equations, we can solve for y:
-(-11/9)-2y=7
11/9-2y=7
-2y=7-11/9
-2y=62/9-11/9
-2y=51/9
Simplifying further, we have:
y=-51/18
Therefore, x = 11/9 and y = -51/18. Since the system has a unique solution for both variables, it is classified as independent.