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

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