elimination problem

Question

- x+14y=3 

x+14y=4

my problem I don't know how they are getting the answer of1/2 from 14.1/4

Answer 1

The Elimination method eliminates a variable because its coefficients are the same (subtraction) or opposite (addition).

 

    -x    +   14y   =   3

     x    +   14y   =   4

---------------------------  [Eliminate x by adding equations]

                28y   =   7

                    y = 1/4      [divide both sides by 28]

 

    -x    +   14y   =   3
     x    +   14y   =   4
---------------------------  [Eliminate y by subtracting equations]

   -2x                =   -1

     x                 =   1/2      [divide both sides by (-2)]

 

Did the problem ask you to solve for x?

Answer 2

Hi Linda,

 

When you add these two equations together (equals added to equals are equal) you get:

 

28y = 7

 

y = 7/28 = 1/4.

 

To get the corresponding x value you have to substitute 1/4 for y in one of the equations and solve for x.

 

So, for example:

 

x + 14 (1/4) = 4

 

Multiply both sides by 4 to clear the equation of fractions (that is one technique for solving an equation containing fraction(s)).

 

4x + 14 = 16

 

4x = 2

 

x = 1/2

 

Check:

 

1/2 + 14(1/4) =? 4

 

2/4 + 14/4  =? 4

 

16/4 =? 4

 

4 = 4

 

So the intersection of the two lines represented by these equations is the ordered pair (1/2, 1/4).