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

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.<br /><br />The given system of equations is:<br />$3x+y=-5$<br />$3y+15=-9x$<br /><br />Step 1: Rearrange the equations in standard form.<br />$3x+y=-5$ can be rearranged as $3x+y+5=0$<br />$3y+15=-9x$ can be rearranged as $9x+3y+15=0$<br /><br />Step 2: Compare the coefficients of the variables in both equations.<br />In the first equation, the coefficient of $x$ is $3$ and the coefficient of $y$ is $1$.<br />In the second equation, the coefficient of $x$ is $9$ and the coefficient of $y$ is $3$.<br /><br />Step 3: Determine the relationship between the coefficients.<br />The coefficients of $x$ and $y$ in the first equation are not proportional to the coefficients of $x$ and $y$ in the second equation.<br /><br />Step 4: Determine the consistency and dependence of the system.<br />Since the coefficients of $x$ and $y$ in the two equations are not proportional, the system of equations is inconsistent.<br /><br />Therefore, the correct answer is:<br />C) inconsistent