Solve the system by substitution.
-$$\begin{array} { l }
16 x - y = 7 \
8 x + 5 y = 31
\end{array}$$
A) $\left\{ \left( \frac { 3 } { 4 } , 5 \right) \right\}$
B){ }
C) $\{ ( 0 , - 7 ) \}$
D) $\{ ( x , y ) \mid y = 16 x - 7 \}$; The equations are dependent

Question

Solve the system by substitution.
-$$\begin{array} { l } 
16 x - y = 7 \
8 x + 5 y = 31
\end{array}$$
A) $\left\{ \left( \frac { 3 } { 4 } , 5 \right) \right\}$
B){ }
C) $\{ ( 0 , - 7 ) \}$
D) $\{ ( x , y ) \mid y = 16 x - 7 \}$; The equations are dependent

Quizplus · Accepted Answer

To solve the system by substitution, we first solve one of the equations for one variable in terms of the other. From the first equation, $16x - y = 7$, we can solve for $y$ to get $y = 16x - 7$. Substituting this expression for $y$ in the second equation, $8x + 5y = 31$, gives us $8x + 5(16x - 7) = 31$. Simplifying this equation allows us to solve for $x$, and then we can find $y$ using the expression $y = 16x - 7$. The solution that fits this process is $\left( \frac{3}{4}, 5 \right)$.

Solve the System by Substitution 16x−y=78x+5y=31\begin{array} { l } 16 x - y = 7 \\8 x + 5 y = 31\end{array}16x−y=78x+5y=31​

Solve the System by Substitution $\begin{array} { l } 16 x - y = 7 \\8 x + 5 y = 31\end{array}$