need a little help

Question

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

x+4y=8

5x+6y=12

Answer 1

You can add/subtract a multiple of one equation to/from another.  This will let you eliminate a variable.

 

(1) x + 4y = 8

(2) 5x + 6y = 12

 

For this problem, we can multiply the first equation by 5:

(1) 5*(x+4y) = 5 * 8

(1) 5x + 20y = 40

 

Now both equations have 5x in them.  Subtract the second equation from this one.  (You can add/subtract either to/from the other.  Subtracting (2) from (1) is easiest because it doesn't produce a bunch of negative numbers in the result.

 

(1) 5x + 20y = 40

(2) 5x +   6y = 12       subtract

     -----------------

             14y = 28       the X term is eliminated

                 y =  2

 

Now you can plug the value for Y back into either of the original equations to get X.  Equation (1) looks easier to work with, so:

 

(1) x + 4y = 8, where y = 2

     x + (4)(2) = 8

     x + 8 = 8

     x = 0

 

The solution is:

(x, y) = (0, 2)

 

      

 

 

 

Answer 2

Hi Pete,

 

x+4y=8       equation 1

5x+6y=12    equation  2

 

Multiply equation 1 by 5

 

5x+20y=40   equation 3

 

subtract equation 2 from equation 3

 

14y =28

 y=28/14=4/2=2

 

substitute y=2 in equation 1

 

x+4y=8

x+4(2)=8

x=8-8=0

 

The solution of the system of equations is x=0 and y=2

 

Check:  x+4y=8

            0+4(2)=8 =8=Right hand side(R.H.S)

 

             5x+6y=12

             5(0)+6(2)=12=12=R.H.S