4x-7y=18 9x-14y=40

Question

Elimination method

 

Answer 1

There is nothing wrong with the way Tamara shows, however, this is the most commonly taught method.  Schools today to not teach - and sometimes not even recognize - other methods. Another way to do this would be the substitution method.

1. Solve for a variable in an equation:

4x - 7y = 18

4x = 7y + 18

x = (7y + 18) / 4

2. Substitute for in other equation:

9((7y + 18) / 4) - 14y = 40

((63y + 162) / 4) -14y = 40

((63y + 162) / 4) - (56y / 4) = 40

(7y + 162) / 4 = 40

7y + 162 = 160

7y = -2

y = -2/7

3. Plug into either equation to solve for other variable:

4x - 7y = 18

4x - 7(-2/7) = 18

4x - (-14/7) = 18

4x + 2 = 18

4x = 16

x = 4

 

I know this looks more complicated, but the equations were set up to look pretty for the elimination method.  In other cases, the substitution method will look prettier.  

Always remember there are many ways to get the right answer.  Apply the simplest! 

 

 

 

 

Answer 2

This linear system of equations consists of the following equations:

     4x - 7y = 18

     9x - 14y = 40

To solve for the system using the elimination method, we need to first multiply one of the equations by a constant that will yield an equation where one of the variables has a coefficient that is the opposite of that variable's coefficient in the other equation. That is, if we multiply the first equation in the system by '-2' then we will generate an equation where the y variable has a coefficient of '+14' which is the opposite of the coefficient of the y variable in the second equation, that being '-14'.

           (-2)·(4x - 7y = 18)

  ==>   (-2)·(4x) - (-2)·(7y) = (-2)·(18) 

            (-8x) - (-14y) = -36

            -8x + 14y = -36

Now we add this equation to the second equation in the system:

          -8x + 14y = -36

    +     9x  - 14y = 40

 ______________________________

   -8x + 9x + 14y - 14y = -36 + 40

     9x - 8x = 40 - 36

           1x = 4     ==>     x = 4

Now that we've solved for x, we plug in its value into one of the two original equations and solve for y:

     4x - 7y = 18     ,        x = 4

     4(4) - 7y = 18

     16 - 7y = 18          subtract 16 from both sides of the equation

     16 - 16 - 7y = 18 - 16

     -7y = 2                 divide both sides of the equation by -7

     -7y/-7 = 2/-7

      y = -2/7

Thus, the solution to the system is (4, -2/7).

We can check the solution by plugging in the values of x and y into one or both original equations:

     4x - 7y = 18

     4(4) - 7(-2/7) = 16 - (-2) = 16 + 2 = 18   

     9x - 14y = 40

     9(4) - 14(-2/7) = 36 - 2(-2) = 36 - (-4) = 36 + 4 = 40