Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $$\left\{ \begin{array} { c }
3 ( x - 4 ) = 8 y \
4 ( 2 y + 3 ) = 3 x
\end{array} \right.$$
A) $( 4 , - 7 )$
B) $( 3,3 )$
C) $( - 1,7 )$
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. $$\left\{ \begin{array} { c } 
3 ( x - 4 ) = 8 y \
4 ( 2 y + 3 ) = 3 x
\end{array} \right.$$
A) $( 4 , - 7 )$
B) $( 3,3 )$
C) $( - 1,7 )$
D)The equations are dependent.
E)The system is inconsistent.

Quizplus · Accepted Answer

Multiply the first equation by $3$ and the second equation by $2$, then we get: $$\left\{ \begin{array} { l }9x-24=24y \ 6x+8y+9x=0\end{array} \right.$$
Adding these two equations gives $24x=24y$, or $y=x$. Substitute into either equation gives $x=3$ and $y=3$, thus the equations are dependent and have infinite solutions, so the correct answer is $\textbf{(D)}$.

Use the Addition Method to Solve the System {3(x−4)=8y4(2y+3)=3x\left\{ \begin{array} { c } 3 ( x - 4 ) = 8 y \\4 ( 2 y + 3 ) = 3 x\end{array} \right.{3(x−4)=8y4(2y+3)=3x​

Use the Addition Method to Solve the System $\left\{ \begin{array} { c } 3 ( x - 4 ) = 8 y \\4 ( 2 y + 3 ) = 3 x\end{array} \right.$