Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
-$\left\{ \begin{array} { c } 4 x + y = 12 \ 16 x + 4 y = 48 \ \text { \end{array} \right.$
A) $\{ ( 5 , - 8 ) \}$
B) infinitely many solutions; $\{ ( x , y ) \mid 4 x + y = 12 \}$ or $\{ ( x , y ) \mid 16 x + 4 y = 48 \}$
C) no solution; $\varnothing$
D) $\{ ( 0,12 ) \}$

Question

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
-$\left\{ \begin{array} { c } 4 x + y = 12 \ 16 x + 4 y = 48 \ \text { \end{array} \right.$
A)  $\{ ( 5 , - 8 ) \}$
B) infinitely many solutions; $\{ ( x , y ) \mid 4 x + y = 12 \}$ or $\{ ( x , y ) \mid 16 x + 4 y = 48 \}$
C) no solution; $\varnothing$
D) $\{ ( 0,12 ) \}$

Quizplus · Accepted Answer

The second equation is a multiple of the first (multiplied by 4), which means they represent the same line. Therefore, there are infinitely many solutions, and the solution set can be represented by either equation.

Solve the System by the Addition Method \(\Left\{ \Begin{array} { C } 4 X + Y =