If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l }
7 x + 8 y = 7 \
14 x + 16 y = 5
\end{array}$$
A) $\left\{ \left\{ x , \frac { 7 } { 8 } - \frac { 7 } { 8 } x \right) \right\}$

B) $\varnothing$

C) $\left\{ \left\{ x , \frac { 1 } { 2 } - \frac { 7 } { 8 } x \right) \right\}$

D) $\{ ( 0,0 ) \}$

Question

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
7 x + 8 y = 7 \
14 x + 16 y = 5
\end{array}$$
A) $\left\{ \left\{ x , \frac { 7 } { 8 } - \frac { 7 } { 8 } x \right) \right\}$

B) $\varnothing$

C) $\left\{ \left\{ x , \frac { 1 } { 2 } - \frac { 7 } { 8 } x \right) \right\}$

D) $\{ ( 0,0 ) \}$

Quizplus · Accepted Answer

The system does not have infinitely many solutions. The second equation is not a multiple of the first, indicating the system is either inconsistent or has a unique solution. Since the coefficients of the second equation are exactly double those of the first, but the constants are not in the same ratio (7 is not half of 5), the system is inconsistent, meaning it has no solution.

If the System Has Infinitely Many Solutions, Write the Solution 7x+8y=714x+16y=5\begin{array} { l } 7 x + 8 y = 7 \\14 x + 16 y = 5\end{array}7x+8y=714x+16y=5​

If the System Has Infinitely Many Solutions, Write the Solution $\begin{array} { l } 7 x + 8 y = 7 \\14 x + 16 y = 5\end{array}$