Solve the problem.
-$$\left\{ \begin{array} { c }
3 x + y = 14 \
12 x + 4 y = 56
\end{array} \right.$$
A) no solution; $\varnothing$
B) $\{ ( 0,14 ) \}$
C) $\{ ( 5 , - 1 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid 3 x + y = 14 \}$ or $\{ ( x , y ) \mid 12 x + 4 y = 56 \}$

Question

Solve the problem.
-$$\left\{ \begin{array} { c } 
3 x + y = 14 \
12 x + 4 y = 56
\end{array} \right.$$
A) no solution; $\varnothing$
B) $\{ ( 0,14 ) \}$
C) $\{ ( 5 , - 1 ) \}$
D) infinitely many solutions; $\{ ( x , y ) \mid 3 x + y = 14 \}$ or $\{ ( x , y ) \mid 12 x + 4 y = 56 \}$

Quizplus · Accepted Answer

The second equation is a multiple of the first (multiplied by 4), so they represent the same line, leading to infinitely many solutions.

Solve the Problem {3x+y=1412x+4y=56\left\{ \begin{array} { c } 3 x + y = 14 \\12 x + 4 y = 56\end{array} \right.{3x+y=1412x+4y=56​

Solve the Problem $\left\{ \begin{array} { c } 3 x + y = 14 \\12 x + 4 y = 56\end{array} \right.$