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. $$\left\{ \begin{array} { c }
7 a + 9 b = 69 \
a = 21 - 5 b
\end{array} \right.$$
A) $( 6,3 )$
B) $( 6 , - 3 )$
C) $( - 6,3 )$
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. $$\left\{ \begin{array} { c } 
7 a + 9 b = 69 \
a = 21 - 5 b
\end{array} \right.$$
A) $( 6,3 )$
B) $( 6 , - 3 )$
C) $( - 6,3 )$
D)The equations are dependent.
E)The system is inconsistent.

Quizplus · Accepted Answer

Substituting $a = 21 - 5b$ into the first equation gives $7(21 - 5b) + 9b = 69$. Simplifying, we get $147 - 35b + 9b = 69$, which simplifies to $-26b = -78$, so $b = 3$. Substituting $b = 3$ back into $a = 21 - 5b$ gives $a = 21 - 15 = 6$, so the solution is $(6, 3)$.

Use the Substitution Method to Solve the Following System {7a+9b=69a=21−5b\left\{ \begin{array} { c } 7 a + 9 b = 69 \\a = 21 - 5 b\end{array} \right.{7a+9b=69a=21−5b​

Use the Substitution Method to Solve the Following System $\left\{ \begin{array} { c } 7 a + 9 b = 69 \\a = 21 - 5 b\end{array} \right.$