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Without graphing, classify the following system as independent, dependent, or inconsistent. -x-2y=7 5x-y=2

A) Independent
B) Dependent
C) Inconsistent
D) None of the above

1 Answer

3 votes

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.

User Ken Shih
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