Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $$\left\{ \begin{array} { l }
6 ( x + 6 ) + 5 ( y - 4 ) = 6 \
6 ( x - 1 ) = - 5 ( y + 2 )
\end{array} \right.$$
A) $( 4,5 )$
B) $( 1 , - 7 )$
C) $( - 4,1 )$
D)The equations are dependent.
E)The system is inconsistent.

Question

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $$\left\{ \begin{array} { l } 
6 ( x + 6 ) + 5 ( y - 4 ) = 6 \
6 ( x - 1 ) = - 5 ( y + 2 )
\end{array} \right.$$
A) $( 4,5 )$
B) $( 1 , - 7 )$
C) $( - 4,1 )$
D)The equations are dependent.
E)The system is inconsistent.

Quizplus · Accepted Answer

First, simplify both equations: 1) $6x + 36 + 5y - 20 = 6$ simplifies to $6x + 5y + 16 = 6$, or $6x + 5y = -10$.2) $6x - 6 = -5y - 10$ simplifies to $6x + 5y = -4$.These two equations, $6x + 5y = -10$ and $6x + 5y = -4$, cannot be true at the same time for any value of $x$ and $y$ because they have the same left-hand side but different right-hand sides. This means the system is inconsistent.

Use the Addition Method to Solve the System {6(x+6)+5(y−4)=66(x−1)=−5(y+2)\left\{ \begin{array} { l } 6 ( x + 6 ) + 5 ( y - 4 ) = 6 \\6 ( x - 1 ) = - 5 ( y + 2 )\end{array} \right.{6(x+6)+5(y−4)=66(x−1)=−5(y+2)​

Use the Addition Method to Solve the System $\left\{ \begin{array} { l } 6 ( x + 6 ) + 5 ( y - 4 ) = 6 \\6 ( x - 1 ) = - 5 ( y + 2 )\end{array} \right.$