Question

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

Answer 1

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,

             $5x+6y=17$..................................(1)

          $-10x-9y=-43$..............................(2)

Step:1

      By elimination method,

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

           $45x+54y=153$.................................(3)

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

           $60x+54y=258$................................(4)

Step:2

       Subtracting the Equations (3) and (4),

              $45x+54y=153$

              $60x+54y=258$

     ( - )

       ( $45x-60x$ ) + ( $54y-54y$ ) = ( $153-258$ )

                               ( $-15x$ ) = ( $-105$ )

                                         $x = 7$

Step:3

      Substitute the x=7 in equation (1),

                            $5x+6y=17$      

                 ( 5 × 7 ) + ( $6y$ ) = 17

                                     $6y$ = -18

                                       $y$ = -3

Step:4

      Check for solution,

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

                               $5x+6y=17$

              ( 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.