SOLUTION: Need help Solving the system by the addition method: 4x + 8y = 6 3x – 8y = 7 7x = 13 I added the x's and the y's cancelled and that left me with 7x=13? I don't think this

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Need help Solving the system by the addition method: 4x + 8y = 6 3x – 8y = 7 7x = 13 I added the x's and the y's cancelled and that left me with 7x=13? I don't think this      Log On


   

Question 202053: Need help Solving the system by the addition method:
4x + 8y = 6
3x – 8y = 7
7x = 13
I added the x's and the y's cancelled and that left me with 7x=13?
I don't think this answer is correct though. Please let me know what I am
doing wrong?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track. You just need to finish up.



Start with the given system of equations:
system%284x%2B8y=6%2C3x-8y=7%29


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


%284x%2B8y%29%2B%283x-8y%29=%286%29%2B%287%29


%284x%2B3x%29%2B%288y-8y%29=6%2B7 Group like terms.


7x%2B0y=13 Combine like terms.


7x=13 Simplify.


x=%2813%29%2F%287%29 Divide both sides by 7 to isolate x.


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


4x%2B8y=6 Now go back to the first equation.


4%2813%2F7%29%2B8y=6 Plug in x=13%2F7.


52%2F7%2B8y=6 Multiply.


cross%287%29%2852%2Fcross%287%29%29%2B7%288y%29=7%286%29 Multiply EVERY term by the LCD 7 to clear any fractions.


52%2B56y=42 Multiply and simplify.


56y=42-52 Subtract 52 from both sides.


56y=-10 Combine like terms on the right side.


y=%28-10%29%2F%2856%29 Divide both sides by 56 to isolate y.


y=-5%2F28 Reduce.


So the solutions are x=13%2F7 and y=-5%2F28.


Which form the ordered pair .


This means that the system is consistent and independent.