Question
Determine whether the system of equations is consistent or inconsistent and ifit is independent or dependent. 3x+y=-5 3y+15=-9x A) consistent and dependent B) consistent and independent C) inconsistent D) inconsistent and dependent
Solution
4
(250 Votos)
Josi
Profissional · Tutor por 6 anos
Resposta
To determine whether the system of equations is consistent or inconsistent and if it is independent or dependent, we need to analyze the given equations.The given system of equations is:
Step 1: Rearrange the equations in standard form.
can be rearranged as
can be rearranged as
Step 2: Compare the coefficients of the variables in both equations.In the first equation, the coefficient of
is
and the coefficient of
is
.In the second equation, the coefficient of
is
and the coefficient of
is
.Step 3: Determine the relationship between the coefficients.The coefficients of
and
in the first equation are not proportional to the coefficients of
and
in the second equation.Step 4: Determine the consistency and dependence of the system.Since the coefficients of
and
in the two equations are not proportional, the system of equations is inconsistent.Therefore, the correct answer is:C) inconsistent