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

classic margarita · Accepted Answer

Final Answer : E, Explanation :  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.

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