Question

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

Answer 1

`2x+5y= 4~~~...(i)\\\\2x-2y = 18~~~...(ii)\\\\(ii) -(i):\\\\~~~~~2x-2y -2x -5y= 18 -4\\\\\implies -7y = 14\\\\\implies y = -\frac{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 = \frac{14}2\\\\\implies x =7\\\\\text{Hence}~ (x,y) =(7,-2).`

Answer 2

y = -2

x = 7

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}`