Use elimination to find the solution to the system of equations.

Question

4x+5y=30

 

5x-6x=36

Answer 1

 4X + 5Y = 30
 
5X  - 6X  = 36

 

Step One... combine like terms in the second equation:
 
    5X  - 6X  = 36

            -1x = 36

 

Step Two... set up this equation for elimination by multiplying / dividing to get the opposite of 4x.  In other words, what do we need to do to -1x to change it into -4x?  In this case multiply by 4.  Since we multiply one side by 4 we need to do it to the other side to keep things equal:

        -1x = 36

    4(-1x) = (4)36

       -4x  = 144

 

Step Three... now we can see there is a -4x in the equation we've worked on, and a +4x in the first equation.  Adding them both up will cancel out (or eliminate) the x component:

      4X + 5Y = 30
     -4x         = 144

      0x + 5y = 444        we get 5y = 444

 

Step Four... solve for y.  Do this by dividing both sides of the equation by 5:

     (5y)/5 = (444)/5

            y = 88.8

 

Step Five... plug in 88.8 into the original first equation to solve for x:

           4X + 5Y = 30
    4x + 5(88.8) = 30

         4x + 444 = 30

  4x +444 -444 = 30 -444

                  4x = -414

               4x/4 = -414/4

                     x= -103.5

 

Finally we arrive at x=-103.5 and y=88.8.  What this means...  If we graph both equations there is exactly one point that will be true for both equations.  This point is located at x,y or (-103.5, 88.8), and is the coordinate location of where they intersect.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

 4X + 5Y = 30

 

5X  - 6X  = 36

 

    X = -36 . From the 2nd equation

   

    4X + 5Y = 30

  4 (- X)  =4( 36)

     5 Y = 4( 36) +30

 

     5Y = 174

 

     y = 174/5 = 34 4/5