Question

Use the method of elimination to solve the pair of simultaneous equation 2x+5y=4,2x-2y=18​

Answer 1

Answer:

              y = -2

              x = 7

Step-by-step explanation:

     Solving simultaneous equation

         2x + 5y = 4 ---------------(I)

         2x - 2y  = 18 -----------(II)

Now, multiply equation (II) by (-1) and then add the equations. So that, 'x' will be eliminated and we can find the value of 'y'

(I)              2x + 5y = 4

(II)*(-1)      -2x  + 2y = - 18 {Now add}

                         7y = -14

                           y = -14/7       {on dividing both sides by 7}

       $\sf \boxed{y= -2}$

Now plugin y = -2 in equation (I)

        2x + 5*(-2) = 4

           2x - 10   = 4

                    2x = 4 + 10     {on adding 10 to both sides}

                    2x = 14

                       x = 14/2      {Divide both sides by 2}

         $\sf \boxed{x = 7}$

Answer 2

$2x+5y= 4~~~...(i)\\\\2x-2y = 18~~~...(ii)\\\\(ii) -(i):\\\\~~~~~2x-2y -2x -5y= 18 -4\\\\\implies -7y = 14\\\\\implies y = -\dfrac{14}7\\\\\implies y= -2\\\\\text{Substitute}~ y=-2~ \text{ in eq (i):}\\\\~~~~~~2x+5(-2) = 4\\\\\implies 2x-10 = 4\\\\\implies 2x = 10+4\\\\\implies 2x =14\\\\\implies x = \dfrac{14}2\\\\\implies x =7\\\\\text{Hence}~ (x,y) =(7,-2).$