Solve the system using the elimination-by-addition method. $$\left( \begin{array} { l }
x + y = 14 \
x - y = 2
\end{array} \right)$$
A) ( 8, 6 )
B) ( 6, 8 )
C) ( 0, 0 )
D) The system is inconsistent.
E) The system is dependent.

Question

Solve the system using the elimination-by-addition method. $$\left( \begin{array} { l } 
x + y = 14 \
x - y = 2
\end{array} \right)$$
A) ( 8, 6 )
B) ( 6, 8 )
C) ( 0, 0 )
D) The system is inconsistent.
E) The system is dependent.

Quizplus · Accepted Answer

We can use the elimination-by-addition method for this system. Adding the two equations results in eliminating the y-term: $$(x + y) + (x - y) = 14 + 2 \Rightarrow 2x = 16 \Rightarrow x = 8.$$ Substituting x = 8 into any of the original equations gives: $$8 + y = 14 \Rightarrow y = 6.$$
Therefore, the solution to the system is (8,6), which corresponds to choice A.

Solve the System Using the Elimination-By-Addition Method (x+y=14x−y=2)\left( \begin{array} { l } x + y = 14 \\x - y = 2\end{array} \right)(x+y=14x−y=2​)

Solve the System Using the Elimination-By-Addition Method $\left( \begin{array} { l } x + y = 14 \\x - y = 2\end{array} \right)$