which classification describes the following system of equations?$\begin{cases}5x + 10y + 15z = 60 \\2x + 4y…

which classification describes the following system of equations?$\begin{cases}5x + 10y + 15z = 60 \\2x + 4y + 6z = 60 \\x + 2y + 3z = 60end{cases}$- inconsistent and dependent- consistent and dependent- consistent and independent- inconsistent and independent

which classification describes the following system of equations?$\begin{cases}5x + 10y + 15z = 60 \\2x + 4y + 6z = 60 \\x + 2y + 3z = 60end{cases}$- inconsistent and dependent- consistent and dependent- consistent and independent- inconsistent and independent

Answer

Explanation:

Step1: Simplify first equation

Divide by 5: $\frac{5x+10y+15z}{5} = \frac{60}{5}$ $x + 2y + 3z = 12$

Step2: Simplify second equation

Divide by 2: $\frac{2x+4y+6z}{2} = \frac{60}{2}$ $x + 2y + 3z = 30$

Step3: Compare simplified equations

The first simplified equation $x+2y+3z=12$ and the third original equation $x+2y+3z=60$ (along with the second simplified $x+2y+3z=30$) are contradictions—they cannot all be true at the same time. Also, the equations are scalar multiples of each other (dependent), but no solution exists.

Answer:

inconsistent and dependent