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3.6.1.html

Steps:


1) Choose one equation and solve for one variable. This is equation #1=

 

2) Substitute the solution using equation #1 into the second equation= and solve for the variable in the equation.

 

3) Using the value from step 2 substitute it in the first equation and solve for the second variable.

 

4) Substitute the values that were found for the variables and solve = for the 3rd unkown variable

 

Example:

 

Step 1) Now that you have 3 equations, choose an equation and solve f= or a  variable.

 

1.    -2x + y + 6z =3D y=

 

2.    3x + 2y +5z =3D 16=  

 

      3.7x+ 3y - 4z=3D 11

 

Step 2) Solve for a variable.

 

1.    -2x + y +6z=3D 1 <= /span>3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" y=3D 2x - 6z +1

 

Now you have your 1st equation.

 

Step 3) Take the 1st equation from step 2 and substitute it into equa= tion 2.

 

3x + 2y + 5z =3D 16 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" 3x + 2(2x - 6z + 1) + 5z = =3D 16

 

Step 4) Combine like terms from step 3. And get the variable x alone = by adding 7z to both sides and dividing 7 to both sides

 

3x + 2(2x - 6z + 1) + 5z =3D 16 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" 7x - 7z =3D 14

7x - 7z (+7z)=3D 14 + 7z 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" 7x =3D 14 + 7z

7x/7 =3D 14/7 + 7z/7 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" x =3D z + 2<= /p>

 

Step 5) Now you have another equation which is number 2

 

x =3D z + 2

 

Step 6) Now take the 1st equation (y=3D 2x - 6z + 1) you solved = for and substitute it into equation 3 ( 7x + 3y - 4z=3D 11).<= /p>

 

7x + 3( 2x - 6z + 1) - 4z =3D 11

 

Step 7) Solve the equation for step six.

 

7x + 3( 2x - 6z + 1) - 4z =3D 11 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" 13x - 22z =3D 8

 

8) Now take equation 2 ( x=3D 2 + z) and substitute it into the equat= ion from step 7 (13x - 22z =3D 8) and solve.

 

13x - 22z =3D 8 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" 13 ( 2 + z ) - 22z = =3D 8

 

z=3D 2

 

9) Now that you have found z (2) plug it into equation 2 ( x =3D z + = 2) to solve for x.

 

x =3D z + 2 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" x =3D 2 + 2

 

x=3D 4

 

10) Now you have two known variables, z and x. Now you can plug it in= to equation 1 (y=3D 2x - 6z +1) to solve for y.

 

y=3D 2x - 6z +1 3D"http://www.browsereditor.com/NetBox/images/math_doublerightarrow.gif" y=3D 2(4) - 6 ( 2) + 1

 

y=3D  -3

 

11) Now you have 3 known variables of x,y,z. These are your solutions ( 4, -3, 2)

 

 

Try This

 

&nb= sp;x-y+z=3D10

3x+= y+2z=3D34

-5x= +2y-z=3D -14

 

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