Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r }
x + 9 y - z = 4 \
5 x + 45 y - 5 z = 20 \
3 x + 27 y - 3 z = 12
\end{array} \right.$$
A) no solution or $\not \supset$
B) $\{ ( 5,3,28 ) \}$
C) infinitely many solutions; dependent equations
D) $\{ ( 3,5,44 ) \}$

Question

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r } 
x + 9 y - z = 4 \
5 x + 45 y - 5 z = 20 \
3 x + 27 y - 3 z = 12
\end{array} \right.$$
A) no solution or $\not \supset$
B) $\{ ( 5,3,28 ) \}$
C) infinitely many solutions; dependent equations
D) $\{ ( 3,5,44 ) \}$

Quizplus · Accepted Answer

The given system of equations is dependent with infinitely many solutions because the second and third equations are multiples of the first equation. This means they represent the same plane in three-dimensional space, leading to an infinite number of solutions where these planes intersect.

Solve the System {x+9y−z=45x+45y−5z=203x+27y−3z=12\left\{ \begin{array} { r } x + 9 y - z = 4 \\5 x + 45 y - 5 z = 20 \\3 x + 27 y - 3 z = 12\end{array} \right.⎩⎨⎧​x+9y−z=45x+45y−5z=203x+27y−3z=12​

Solve the System $\left\{ \begin{array} { r } x + 9 y - z = 4 \\5 x + 45 y - 5 z = 20 \\3 x + 27 y - 3 z = 12\end{array} \right.$