Solve the system of linear equations below by the method of elimination, if a single solution exists. $\left\{ \begin{array} { c }
- x + 2 y = 3 \
- 2 x + 4 y = 8
\end{array} \right.$
A) $x = 9 \text { and } y = - 8$
B) $x = - 5 \text { and } y = - 1$
C) $x = 2 \text { and } y = 6$
D) $x = - 4 \text { and } y = 8$
E)Infinitely many solutions

Question

Solve the system of linear equations below by the method of elimination, if a single solution exists. $\left\{ \begin{array} { c } 
- x + 2 y = 3 \
- 2 x + 4 y = 8
\end{array} \right.$
A) $x = 9 \text { and } y = - 8$
B) $x = - 5 \text { and } y = - 1$
C) $x = 2 \text { and } y = 6$
D) $x = - 4 \text { and } y = 8$
E)Infinitely many solutions

Quizplus · Accepted Answer

The second equation is a multiple of the first (multiplying the first equation by 2 gives the second equation), indicating that both equations represent the same line. Therefore, there are infinitely many solutions, as every point on the line is a solution to the system of equations.

Solve the System of Linear Equations Below by the Method {−x+2y=3−2x+4y=8\left\{ \begin{array} { c } - x + 2 y = 3 \\- 2 x + 4 y = 8\end{array} \right.{−x+2y=3−2x+4y=8​

Solve the System of Linear Equations Below by the Method $\left\{ \begin{array} { c } - x + 2 y = 3 \\- 2 x + 4 y = 8\end{array} \right.$