Solve the system of linear equations below by the method of elimination, if a single solution exists. { − 9 u − 8 v = − 8 9 u + 2 v = 2 \left\{ \begin{array} { c } - 9 u - 8 v = - 8 \9 u + 2 v = 2\end{array} ight. { − 9 u − 8 v = − 8 9 u + 2 v = 2 A) u = 8 and v = − 2 u = 8 ext { and } v = - 2 u = 8 and v = − 2 B) u = − 3 and v = 5 u = - 3 ext { and } v = 5 u = − 3 and v = 5 C) u = − 6 and v = 7 u = - 6 ext { and } v = 7 u = − 6 and v = 7 D) u = 0 and v = 1 u = 0 ext { and } v = 1 u = 0 and v = 1 E) no solution

Question

Solve the system of linear equations below by the method of elimination, if a single solution exists.   { − 9 u − 8 v = − 8 9 u + 2 v = 2 \left\{ \begin{array} { c } - 9 u - 8 v = - 8 \9 u + 2 v = 2\end{array} ight. { − 9 u − 8 v = − 8 9 u + 2 v = 2 ​ A)    u = 8  and  v = − 2 u = 8 	ext { and } v = - 2 u = 8  and  v = − 2 B)    u = − 3  and  v = 5 u = - 3 	ext { and } v = 5 u = − 3  and  v = 5 C)    u = − 6  and  v = 7 u = - 6 	ext { and } v = 7 u = − 6  and  v = 7 D)    u = 0  and  v = 1 u = 0 	ext { and } v = 1 u = 0  and  v = 1 E) no solution

Zybrea Knight · Accepted Answer

Final Answer : D, Explanation :  Multiplying the second equation by $4$ we get, $36u+8v=8$. Adding this to the first equation which is $-9u-8v=-8$ gives $27u=0$ which implies $u=0$. Substituting the value of $u$ in any one equation above we get $v=1$. Thus the solution is $(u,v)=(0,1)$. Therefore, the answer is D.

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