substitution method 4y=x and 4x+3y=19

Question

substitution method 4y=x and 4x+3y=19

Answer 1

Working to solve two equations, the substitution method rearranges (if necessary) one equation into a form where one side appears in the second equation.  Then, the other side of that equation is placed into the second equation where that expression appears.

Looking at these two equations:
      (a) the first eq has an ‘x’ that appears in the second eq
      (b) the first eq has a ‘y’ that appears in the second eq

Let’s use information (a) first:

     Substituting 4y for x (because they are equal) in the second eq, we get:
             4 (4y) + 3y = 19
                16y + 3y  = 19
                      y =1

          Then, using the first eq so we can find x,
                     4y = x
                     4(1) = x
                       x = 4

Information (b) will produce the same answer:

      Substituting x/4 for y (I solved for y) in the second eq, we get:
                 4x  + 3(x/4)  = 19
                  16x  + 3x  =  76     (multiplied everything by 4 to get rid of fraction)
                       19x = 76
                           x = 4

       So, again using the first eq,    y = 1

Now, decide which method you like better.  You will learn to recognize this in advance.

Checking:
     Does   4(y) = x    ?
                 4(1)  =  4     ?     yes

     Does    4x  +  3y  =  19   ?
                  4(4) + 3(1)  =  19    ?    …   yes