Question

Which of the following systems is dependent? x − y = 2 and x + y = −2 x − y = 2 and −2x + 2y = −4 x − y = 2 and 3x − 3y = 2 x − y = 2 and −x − y = −2

Answer 1

the following system is dependent:

x - y = 2 and -2x + 2y = -4

Answer 2

A system is linearly dependent, when multiplying one of the equations by a scalar, you get the other equation.
We then have the following system of equations:

`x - y = 2 -2x + 2y = -4`
Let's rewrite the system of equations.
To do this, let's multiply equation 1 by scalar -2:

`-2x - (-2) y = (-2) 2 -2x + 2y = -4`
We observe that we obtain equation 2 of the system.
Therefore, the system is linearly dependent.
Answer:
the following system is dependent:
x - y = 2 and -2x + 2y = -4