Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
-$$\begin{array} { r }
x + 8 y = 37 \
5 x + 7 y = 20
\end{array}$$
A) $\{ ( - 3,5 ) \}$
B) $\{ ( - 4,6 ) \}$
C) $\{ ( x , y ) \mid x + 8 y = 37 \}$
D) $\varnothing$

Question

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
-$$\begin{array} { r } 
x + 8 y = 37 \
5 x + 7 y = 20
\end{array}$$
A) $\{ ( - 3,5 ) \}$
B) $\{ ( - 4,6 ) \}$
C) $\{ ( x , y ) \mid x + 8 y = 37 \}$
D) $\varnothing$

Quizplus · Accepted Answer

We can solve the system using substitution or elimination. Using elimination, we can multiply the first equation by 5 and the second equation by -1, and then add the two equations together to eliminate the x variable:

$$\begin{array} { r } 
5 x + 40 y = 185 \
-5 x - 7 y = -20 \
\end{array}$$

Adding these equations gives:

$$33 y = 165$$

Dividing by 33 gives:

$$y=5$$

Substituting this value for y into either equation gives:

$$x + 8(5) = 37$$

Which simplifies to:

$$x = -3$$

Therefore, the solution to the system is:

$$\{(-3,5)\}$$

which is given in choice A.

Solve the System by the Method of Your Choice x+8y=375x+7y=20\begin{array} { r } x + 8 y = 37 \\5 x + 7 y = 20\end{array}x+8y=375x+7y=20​

Solve the System by the Method of Your Choice $\begin{array} { r } x + 8 y = 37 \\5 x + 7 y = 20\end{array}$