-4x+y=6, -5x-y=21

Question

solving systems of equations by substitution and we are stuck

Answer 1

-4x+y=6             [eq1]

-5x-y=21             [eq2]

 

To solve this system of equations using substitution, you must first solve for a variable in one equation, then substitute that expression into the other equation.

 

Solve for y in eq1:

     y = 4x+6

 

Substitute that into eq2:

    -5x - (4x+6) = 21

     -9x - 6 = 21                [collect terms]

      -9x = 27                 [add 6 to both sides]

         x = -3               [divide both sides by (-9)]

 

Now, substitute for x in either eq1 or eq2:

          -4x+y=6             [eq1]

           -4(-3) + y = 6

               12 + y = 6

              y = -6

 

Check (very important):

  Is   -4(-3)+(-6) = 6   ?

           12 - 6 = 6   ?

               6 = 6   ?yes

  Is   -5x-y=21     ?

        -5(-3)-(-6) = 21   ?

           15 + 6 = 21   ?

              21 = 21   ?yes

Answer 2

You can solve these easily by adding the two equations.  You can see that one equation has a + y and the other a - y that will cancel out nicely:

 

-4x + y = 6

-5x - y = 21

 

Add these together

 

-9x = 27

 

Now solve for x.  Then plug x into either equation and solve for y to get your y value.

 

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