Solve Linear Systems by Addition
-$$\begin{array} { l }
6 x + 8 y = 8 \
6 x - 2 y = - 2
\end{array}$$
A) $\{ ( 0,1 ) \}$
B) $\{ ( 1,0 ) \}$
C) $\{ ( 1,1 ) \}$
D) $\{ ( 0,0 ) \}$

Question

Solve Linear Systems by Addition
-$$\begin{array} { l } 
6 x + 8 y = 8 \
6 x - 2 y = - 2
\end{array}$$
A) $\{ ( 0,1 ) \}$
B) $\{ ( 1,0 ) \}$
C) $\{ ( 1,1 ) \}$
D) $\{ ( 0,0 ) \}$

Quizplus · Accepted Answer

To solve the system by addition, we can add the two equations together to eliminate $x$. Adding them gives $6x + 8y + 6x - 2y = 8 - 2$, which simplifies to $12x + 6y = 6$. This step is incorrect; the correct approach is to directly add the two equations: $6x + 8y + 6x - 2y = 8 - 2$, simplifying to $12x + 6y = 6$ is not the right simplification after adding. The correct process is: Adding the two equations directly gives $6x + 8y + 6x - 2y = 8 - 2$, which simplifies to $12x + 6y = 6$, which is incorrect. The correct simplification after adding the equations is $12x + 6y = 6$, which is not the step involved here; instead, we should correctly add or subtract the equations to eliminate one variable. The correct steps are: Subtract the second equation from the first to eliminate $x$, resulting in $10y = 10$, which gives $y = 1$. Substituting $y = 1$ into one of the original equations to solve for $x$ gives $x = 0$. Therefore, the solution is $\{(0,1)\}$.

Solve Linear Systems by Addition - 6x+8y=86x−2y=−2\begin{array} { l } 6 x + 8 y = 8 \\6 x - 2 y = - 2\end{array}6x+8y=86x−2y=−2​

Solve Linear Systems by Addition
- $\begin{array} { l } 6 x + 8 y = 8 \\6 x - 2 y = - 2\end{array}$