Question

is the system independent, dependent, or inconsistent?

Answer 1

Here there are two linear equations with two variables - so the system is a 2D system.

A system is inconsistent if the two lines are parallel but have different y intercepts.

A system is independent if the lines cross at one point only

A system is dependent if the lines are really running on top of each other.

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So start by solving the equations for y = mx + c to assess their slopes (m) and their y intercept (c).

y = -x + 5 - (1) slope m = -1; intercept c = 5

-3y = 3x - 15 - (2)

3y = -3x + 15

y = -x + 5 slope m = -1; intercept c = 5.

Since (1) = (2) then the equations represent the same line so the system is dependent.

Answer 2

thank you so much for the explination!

Answer 3

Anytime.