Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { l }
5 ( x - 1 ) + 23 = 43 - 3 y \
9 ( x + 1 ) + 35 = 82 - 4 y
\end{array} \right.$$
A) $( 2,5 )$
B) $( 5,2 )$
C) $( - 2 , - 5 )$
D)The equations are dependent.
E)The system is inconsistent.

Question

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { l } 
5 ( x - 1 ) + 23 = 43 - 3 y \
9 ( x + 1 ) + 35 = 82 - 4 y
\end{array} \right.$$
A) $( 2,5 )$
B) $( 5,2 )$
C) $( - 2 , - 5 )$
D)The equations are dependent.
E)The system is inconsistent.

Quizplus · Accepted Answer

First, simplify both equations: 1) $5(x - 1) + 23 = 43 - 3y$ becomes $5x - 5 + 23 = 43 - 3y$, which simplifies to $5x + 18 = 43 - 3y$, and further to $5x = 25 - 3y$.2) $9(x + 1) + 35 = 82 - 4y$ becomes $9x + 9 + 35 = 82 - 4y$, which simplifies to $9x + 44 = 82 - 4y$, and further to $9x = 38 - 4y$.From the first equation, we can express $x$ in terms of $y$: $x = 5 - \frac{3}{5}y$.Substituting $x$ from the first equation into the second gives a single equation in $y$, which can be solved to find the value of $y$, and then $x$ can be determined using the value of $y$. Solving these equations yields the solution $(2, 5)$.

Use the Substitution Method to Solve the Following System {5(x−1)+23=43−3y9(x+1)+35=82−4y\left\{ \begin{array} { l } 5 ( x - 1 ) + 23 = 43 - 3 y \\9 ( x + 1 ) + 35 = 82 - 4 y\end{array} \right.{5(x−1)+23=43−3y9(x+1)+35=82−4y​

Use the Substitution Method to Solve the Following System $\left\{ \begin{array} { l } 5 ( x - 1 ) + 23 = 43 - 3 y \\9 ( x + 1 ) + 35 = 82 - 4 y\end{array} \right.$