SOLUTION: My study question asks....Solve the following systems of equation by any method. All I am asking for is the name of a method so I can look up the order or way to solve it.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: My study question asks....Solve the following systems of equation by any method. All I am asking for is the name of a method so I can look up the order or way to solve it.       Log On


   

Question 130331: My study question asks....Solve the following systems of equation by any method.
All I am asking for is the name of a method so I can look up the order or way to solve it.
3x-2y=12
and
2x+y=8
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can solve this by substitution, elimination, or graphing


Let's solve this system by substitution






Start with the given system of equations:

system%283x-2y=12%2C2x%2By=8%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

3x-2y=12 Start with the first equation


-2y=12-3x Subtract 3x from both sides


-2y=-3x%2B12 Rearrange the equation


y=%28-3x%2B12%29%2F%28-2%29 Divide both sides by -2


y=%28%28-3%29%2F%28-2%29%29x%2B%2812%29%2F%28-2%29 Break up the fraction


y=%283%2F2%29x-6 Reduce



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

Since y=%283%2F2%29x-6, we can now replace each y in the second equation with %283%2F2%29x-6 to solve for x



2x%2Bhighlight%28%28%283%2F2%29x-6%29%29=8 Plug in y=%283%2F2%29x-6 into the first equation. In other words, replace each y with %283%2F2%29x-6. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



%282%29%282x%2B%283%2F2%29x-6%29=%282%29%288%29 Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



4x%2B3x-12=16 Distribute and multiply the LCM to each side



7x-12=16 Combine like terms on the left side


7x=16%2B12Add 12 to both sides


7x=28 Combine like terms on the right side


x=%2828%29%2F%287%29 Divide both sides by 7 to isolate x



x=4 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=4









Since we know that x=4 we can plug it into the equation y=%283%2F2%29x-6 (remember we previously solved for y in the first equation).



y=%283%2F2%29x-6 Start with the equation where y was previously isolated.


y=%283%2F2%29%284%29-6 Plug in x=4


y=12%2F2-6 Multiply


y=6-6 Reduce


y=0 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=0









-----------------Summary------------------------------

So our answers are:

x=4 and y=0

which form the point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 3x-2y=12 (red) and 2x%2By=8 (green) and the intersection of the lines (blue circle).