What is the solution of the system? Use elimination.
5x + 6y = 17
−10x − 9y = −43

By using elimination method the solution for the given equations 5x+6y=17 and -10x-9y= -43 are x=7 and y= -3.

Step-by-step explanation:

The given equations are,

             ..................................(1)

          ..............................(2)

Step:1

      By elimination method,

     Multiplying the equation (1) by 9            ( Eqn (1) × 9)

           .................................(3)

     Multiplying the equation (2) by -6         ( Eqn (2) × -6)

           ................................(4)

Step:2

       Subtracting the Equations (3) and (4),

     ( - )

       ( ) + ( ) = ( )

                               ( ) = ( )

Step:3

      Substitute the x=7 in equation (1),

                 ( 5 × 7 ) + ( ) = 17

                                      = -18

                                        = -3

Step:4

      Check for solution,

       Substitute the x and y values in Eqn (1),

              ( 5 × 7 ) + ( 6 × -3 ) = 17

                        ( 35 ) - ( 18 ) = 17

                                        17 = 17

Result:

        The solution for the equations 5x+6y=17 and -10x-9y= -43 are x=7 and y= -3.

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