Solve the system by the method of substitution. { x 2 + y 2 = 25 − 6 x + y = 5 \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \- 6 x + y = 5\end{array} ight. { x 2 + y 2 = 25 − 6 x + y = 5 A) ( 0 , 25 ) , ( − 30 , − 175 ) ( 0,25 ) , ( - 30 , - 175 ) ( 0 , 25 ) , ( − 30 , − 175 ) B) ( 0 , 5 ) , ( 30 , 185 ) ( 0,5 ) , ( 30,185 ) ( 0 , 5 ) , ( 30 , 185 ) C) ( 0 , 5 ) , ( − 60 37 , − 175 37 ) ( 0,5 ) , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } ight) ( 0 , 5 ) , ( − 37 60 , − 37 175 ) D) ( 0 , 25 ) , ( − 60 37 , − 175 37 ) ( 0,25 ) , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } ight) ( 0 , 25 ) , ( − 37 60 , − 37 175 ) E) no solution exists

Question

Solve the system by the method of substitution.   { x 2 + y 2 = 25 − 6 x + y = 5 \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \- 6 x + y = 5\end{array} ight. { x 2 + y 2 = 25 − 6 x + y = 5 ​ A)    ( 0 , 25 )  , ( − 30 , − 175 )  ( 0,25 )  , ( - 30 , - 175 )  ( 0 , 25 )  , ( − 30 , − 175 )  B)    ( 0 , 5 )  , ( 30 , 185 )  ( 0,5 )  , ( 30,185 )  ( 0 , 5 )  , ( 30 , 185 )  C)    ( 0 , 5 )  , ( − 60 37 , − 175 37 )  ( 0,5 )  , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } ight)  ( 0 , 5 )  , ( − 37 60 ​ , − 37 175 ​ )  D)    ( 0 , 25 )  , ( − 60 37 , − 175 37 )  ( 0,25 )  , \left( - \frac { 60 } { 37 } , - \frac { 175 } { 37 } ight)  ( 0 , 25 )  , ( − 37 60 ​ , − 37 175 ​ )  E) no solution exists

Bindhu Satheesh · Accepted Answer

Final Answer : C, Explanation :   From the second equation, we can express   y y y   in terms of   x x x  :   y = 6 x + 5 y = 6x + 5 y = 6 x + 5  . Substituting this into the first equation gives   x 2 + ( 6 x + 5 ) 2 = 25 x^2 + (6x + 5)^2 = 25 x 2 + ( 6 x + 5 ) 2 = 25  . Solving this equation for   x x x   and then finding the corresponding   y y y   values, we get two solutions:   ( 0 , 5 ) (0,5) ( 0 , 5 )   and   ( − 60 37 , − 175 37 ) \left(-\frac{60}{37}, -\frac{175}{37}\right) ( − 37 60 ​ , − 37 175 ​ )  .

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