2y+4x=8 ;x=-2,1,3

Question

I am really confused to this question can someone explain to me step by step please!

Answer 1

In this problem we are given an equation in x any y (2y +4x =8) and three values of x (-2, 1, 3).

 For each value of x we are required to find the corresponding value of y that would make the given equation TRUE.

First value of x=-2

Second value of x=1

Third value of x= 3

First choose the first value of x. That is x=-2. Now substitute x=-2 into the equation 2y +4x =8

            we have 2y + 4(-2)=8, ( note 4 times  -2 equals -8).

Thus we have  2y -8 =8 . Now we add 8 to both sides of the equation to leave just the term in y on the left side of equal sign. 2y -8 +8 = 8+8 ;

    this is equal to: 2y = 16 ; Now to find for y we have to divide both sides by 2: this gives

 2y/2 = 16/2 ; finally y = 8.  We therefore found that when x=-2 then y= 8.

We can check our answer by substituting x =-2 and y =8 in the equation (2y +4x =8) to see if the equation is true. Substituting we have, 2(8) + 4(-2) = 8 ;  which is 16 -8 =8 ; which is 8=8  ; which is true.     

The above procedure is repeated for the second and third values of x. 

 

Answer 2

     2y + 4x  =  8    

          - 4x      - 4x

   ________________

            2y  =  8 - 4x

     (2y) / 2  =  (8 - 4x) / 2  =  (8) / 2  -  (4x) / 2

              y  =  4 - 2x

     y  =  4 - 2x   ;   x = -2, 1, 3

 ==>   x  =  -2

           y  =  4  -  2·(-2)  

              =  4  -  (-4)  

              =  4  +  4  

          y  =  8

 ==>   x  =  1

           y  =  4  -  2·(1)  

              =  4  -  2  

          y  =  2

 ==>   x  =  3

           y  =  4  -  2·(3)

              =  4  -  6  

          y  =  -2 

Answer 3

I am assuming that you are supposed to find the value of y for each suggested value of x (as Kevin suggested).

2y + 4x = 8                    Given

2y + 4x - 4x = 8 - 4x       Subtract 4x from each side

2y = 8 - 4x                     Simplify

2y/2 = (8 - 4x)/2            Divide each side by 2

2y/2 = 8/2 - 4x/2           Distribute the /2

y = 4 - 2x                     Simplify

Now that the equation is solved for y, I am going to substitute for each of the values of x given above

y = 4 - 2x         y = 4 - 2x           y = 4 -2x       Given equation solved for y

y = 4 - 2(-2)     y = 4 - 2(1)        y = 4 - 2(3)   Substitution of each value of x

y = 4 + 4          y = 4 -2             y = 4 - 6        Simplify (multiplication)

y = 8               y = 2                 y = -2             Simplify (addition/subtraction)

As sets of ordered pairs, the answers are {(-2,8),(1,2),(3,-2)}