2x-7y=21 -x-2y=6 solve by substitution

Question

please help not sure how to set up. thank you

Answer 1

 2X - 7Y = 21

 - X - 2Y = 6

 

 

   From 2nd equation:

     X = -2y -6

 

    Substitute  X in first equation

 

     2 ( -2Y - 6 ) - 7 Y = 21

 

      -4y - 12 -7y = 21

     

       -11 y = 33

         

        y = - 33  = - 3

                11

   Substitute X- value back into 2nd  equation:

 

       X = -2( -3) -6 =0

    

     The answer ( X,y) = (0, -3)

 

     Testing The answer:

 

      2( 0 ) - 7( -3) = 21

 

      - 0 - 2( -3 ) = 6

Answer 2

2x-7y=21

-x-2y=6

 

Take either equation and solve for either variable. Then take the expression equal to that variable and substitute it for the variable in the other equation.

 

Let's solve for x in the second equation:

-x-2y=6

-2y=6+x

-2y-6=x

 

Now substitute in first equation:

2(-2y-6)-7y=21

-4y-12-7y=21

Collect the y terms and add 12 to both sides:

-11y=33

Divide both sides by -11:

y = -3

 

Now that we know y we can substitute it to find x:

-2(-3)-6=x

x=0

 

So the solution to the system of equations is the point (0,-3).

 

Answer 3

-x - 2y = 6

2x -7y = 21

 

From -x - 2y =6,  adding 2y to both sides,  -x = 6+2y,  or x = -6 - 2y

 

From 2x - 7y = 21,    2(-6 -2y) - 7y = 21,    so  -12 -11y = 21,   -11y = 33,  so y = -3

 

From -x - 2y = 6,   -x + 6 = 6, so  x = 0.

 

x = 0,  y = -3