Start with the given system of equations:



Multiply the both sides of the first equation by 2.


Distribute and multiply.


So we have the new system of equations:



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:





Group like terms.


Combine like terms.


Simplify.


Divide both sides by to isolate .


Reduce.


------------------------------------------------------------------


Now go back to the first equation.


Plug in .


Multiply.


Add to both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


So the solutions are and .


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of (red) and (green)

solve the system analytically: 
 
 x +  y +  z = 10
2x + 6y + 2z = 40
-x + 7y -... (answered by Edwin McCravy)

Can I please get some assistance for this problem? Thank you. 

Solve the following... (answered by Edwin McCravy,stanbon)

Solve the system of eqations. 
x + y = -4 
x - y =... (answered by checkley77)

Solve the system of eqations.

x + y = -4

x - y =... (answered by checkley77)

solve the system of eqations
1/3x + 1/3y = 1
x-7 =... (answered by checkley77)

Would you please help me solve this equation:

Solve the system analytically:
x+y+z=-4
 (answered by ankor@dixie-net.com,mananth)

Use the substitution to solve the following system

x+7y=2... (answered by checkley77)

Solve this system of linear equations using the elimination method.  Be sure to show all... (answered by Boreal)

Solve the system of linear equations using matrices.

x+7y=6
x+6y=2... (answered by jorel1380)