Solve the system by using the substitution method. $$\left( \begin{array} { c }
4 x - 12 y = - 16 \
2 x - 6 y = - 8
\end{array} \right)$$
A) $( 5 , - 6 )$
B) $\{ ( x , y ) \mid 4 x - 12 y = - 16 \}$
C) $( 16,0 )$
D) $( - 7,7 )$
E) inconsistent

Question

Solve the system by using the substitution method. $$\left( \begin{array} { c } 
4 x - 12 y = - 16 \
2 x - 6 y = - 8
\end{array} \right)$$
A) $( 5 , - 6 )$
B) $\{ ( x , y ) \mid 4 x - 12 y = - 16 \}$
C) $( 16,0 )$
D) $( - 7,7 )$
E) inconsistent

Quizplus · Accepted Answer

The two equations are essentially the same (the second is a multiple of the first), meaning any solution that satisfies one will satisfy the other. This results in an infinite number of solutions along the line described by $4x - 12y = -16$, rather than a single solution point.

Solve the System by Using the Substitution Method (4x−12y=−162x−6y=−8)\left( \begin{array} { c } 4 x - 12 y = - 16 \\2 x - 6 y = - 8\end{array} \right)(4x−12y=−162x−6y=−8​)

Solve the System by Using the Substitution Method $\left( \begin{array} { c } 4 x - 12 y = - 16 \\2 x - 6 y = - 8\end{array} \right)$