SOLUTION: 2x-5y=-6 8x+3y=68 solve the system of equations and enter the solution as an ordered pair.

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Question 174146: 2x-5y=-6
8x+3y=68
solve the system of equations and enter the solution as an ordered pair.
Found 3 solutions by jim_thompson5910, jojo14344, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%282x-5y=-6%2C8x%2B3y=68%29


-4%282x-5y%29=-4%28-6%29 Multiply the both sides of the first equation by -4.


-8x%2B20y=24 Distribute and multiply.


So we have the new system of equations:
system%28-8x%2B20y=24%2C8x%2B3y=68%29


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


%28-8x%2B20y%29%2B%288x%2B3y%29=%2824%29%2B%2868%29


%28-8x%2B8x%29%2B%2820y%2B3y%29=24%2B68 Group like terms.


0x%2B23y=92 Combine like terms. Notice how the x terms cancel out.


23y=92 Simplify.


y=%2892%29%2F%2823%29 Divide both sides by 23 to isolate y.


y=4 Reduce.


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


-8x%2B20y=24 Now go back to the first equation.


-8x%2B20%284%29=24 Plug in y=4.


-8x%2B80=24 Multiply.


-8x=24-80 Subtract 80 from both sides.


-8x=-56 Combine like terms on the right side.


x=%28-56%29%2F%28-8%29 Divide both sides by -8 to isolate x.


x=7 Reduce.


So our answer is x=7 and y=4.


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 2x-5y=-6 (red) and 8x%2B3y=68 (green)

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

2x-5y=-6+------------>EQN 1, y=%282x%2B6%29%2F5=%282%2F5%29x%2B%286%2F5%29
8x%2B3y=68------------->EQN 2, y=%28-8x%2B68%29%2F3=%28-8%2F3%29x%2B%2868%2F3%29
In EQN 1 we get:
2x=5y-6, transpose terms and isolate "x"
cross%282%29x%2Fcross%282%29=%285y-6%29%2F2, divide the whole eqn by 2
x=%285%2F2%29y-%286%2F2%29=%285%2F2%29y-3--------------> EQN 3
Subst. EQN 3 in EQN 2:
8%28%285%2F2%29y-3%29%2B3y=68
%2840%2F2%29y-24%2B3y=68
20y-24%2B3y=68, combine similar terms
23y=68%2B24=92
cross%2823%29y%2Fcross%2823%29=cross%2892%294%2Fcross%2823%29
highlight%28y=4%29, subst. in EQN 3:
x=%285%2F2%29%284%29-3=%2820%2F2%29-3=10-3
highlight%28x=7%29
So the ordered pair -----> (7,4)
Let's see the graph:

Thanky ou,
Jojo

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x-5y=-6
8x+3y=68
----------------
|x y +1|
|2 -5 6| = 0
|8 3 -68|
DET = 6+40 = 46
------------------
x*DET = 340-18
x = 7
-------
-y*DET = -136-48
y = 4