Solve the system.
-$$\left\{ \begin{array} { l }
7 x - 2 y = 5 \
28 x - 8 y = 15
\end{array} \right.$$
A) inconsistent (no solution)
B) $( 6 , - 9 )$
C) $( 2,5 )$
D) consistent (many solutions)

Question

Solve the system.
-$$\left\{ \begin{array} { l } 
7 x - 2 y = 5 \
28 x - 8 y = 15
\end{array} \right.$$
A) inconsistent (no solution)
B) $( 6 , - 9 )$
C) $( 2,5 )$
D) consistent (many solutions)

Quizplus · Accepted Answer

The second equation is simply the first equation multiplied by 4, which means both lines represent the same line in a graphical representation. However, when you actually multiply the first equation by 4 to compare it directly to the second, you get $28x - 8y = 20$, not $28x - 8y = 15$ as given in the second equation. This discrepancy indicates that there has been a mistake in the system's setup, suggesting the system is actually inconsistent because no single (x, y) pair can satisfy both equations due to the contradiction in their constants (5 vs. 15 when scaled).

Solve the System {7x−2y=528x−8y=15\left\{ \begin{array} { l } 7 x - 2 y = 5 \\28 x - 8 y = 15\end{array} \right.{7x−2y=528x−8y=15​

Solve the System $\left\{ \begin{array} { l } 7 x - 2 y = 5 \\28 x - 8 y = 15\end{array} \right.$