Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l }
y = 15 - 4 x \
16 x + 4 y = 60
\end{array}$$
A) $\{ ( 0,15 ) \}$
B) $\{ ( 5 , - 5 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 15 \}$
D) $\varnothing$ )

Question

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
y = 15 - 4 x \
16 x + 4 y = 60
\end{array}$$
A) $\{ ( 0,15 ) \}$
B) $\{ ( 5 , - 5 ) \}$
C) $\{ ( x , y ) \mid 4 x + y = 15 \}$
D) $\varnothing$ )

Quizplus · Accepted Answer

The system given is a pair of linear equations. When we manipulate the second equation to isolate y, we get $y = 15 - 4x$, which is identical to the first equation. This means every solution to one equation is a solution to the other, resulting in an infinite number of solutions (all points on the line $y = 15 - 4x$), not exactly one ordered-pair solution. Option C correctly represents this infinite set of solutions.

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution y=15−4x16x+4y=60\begin{array} { l } y = 15 - 4 x \\16 x + 4 y = 60\end{array}y=15−4x16x+4y=60​

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution $\begin{array} { l } y = 15 - 4 x \\16 x + 4 y = 60\end{array}$