how do you solve systems of equations using elimination and substitution

Question

how do you solve 6x+3y=9 and 2x+3y=1  using system of equations

 

Answer 1

To solve this you first find either Y with respect to X or vice versa. I would start with 2x + 3y = 1.

 

2x+3y=1

3y=1-2x

y=(1-2x)/3

 

Now that we have an expression for Y we can plug it in to the other equation.

 

6x + 3y = 9

6x + 3*[(1-2x)/3] = 9       You can see that there will be some cancellation here.

 

I believe it should be fairly clear from here. By plugging in the expression for Y you can solve for X. Once finding a value for X you can then plug that back in to the expression for Y thereby finding the value of each. Hope this was helpful.

Answer 2

 6X + 3Y =9

 2X +  3Y =1

 

   By elimination method, in which by multiplying one equation and adding both in such a way that one

    variable gets eliminated, and 2 equation gets converted to one, and after solving one substitute in other

    to get the 2nd one.

 

          6x + 3y =9

    -1( 2X  + 3y = 1)       Multiply 2nd equation by (-1) , and add 2 equations together.

    --------------------

       4X = 8       X=2

 

  Substitute   X= 2 in first equation:

   6(2) + 3Y = 9 

    3Y = -3            Y = -1/

To test the answers: have to place the obtained values in original equation, it should satisfy the equality.

    6(2) + 3 ( -1) = 9

     2(2) +3 (-1)  = 1      Therefore, the answers are correct.