SOLUTION: 5x + 3y = 23 2x + 4y = 12 Please help me figure out what the x and y are. my teacher wants me to present my answer to the class tomorrow and how i did it. Thanks in advance.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 5x + 3y = 23 2x + 4y = 12 Please help me figure out what the x and y are. my teacher wants me to present my answer to the class tomorrow and how i did it. Thanks in advance.      Log On


   

Question 556418: 5x + 3y = 23
2x + 4y = 12
Please help me figure out what the x and y are. my teacher wants me to present my answer to the class tomorrow and how i did it.
Thanks in advance.
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%285x%2B3y=23%2C2x%2B4y=12%29


4%285x%2B3y%29=4%2823%29 Multiply the both sides of the first equation by 4.


20x%2B12y=92 Distribute and multiply.


-3%282x%2B4y%29=-3%2812%29 Multiply the both sides of the second equation by -3.


-6x-12y=-36 Distribute and multiply.


So we have the new system of equations:
system%2820x%2B12y=92%2C-6x-12y=-36%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:


%2820x%2B12y%29%2B%28-6x-12y%29=%2892%29%2B%28-36%29


%2820x%2B-6x%29%2B%2812y%2B-12y%29=92%2B-36 Group like terms.


14x%2B0y=56 Combine like terms.


14x=56 Simplify.


x=%2856%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=4 Reduce.


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


20x%2B12y=92 Now go back to the first equation.


20%284%29%2B12y=92 Plug in x=4.


80%2B12y=92 Multiply.


12y=92-80 Subtract 80 from both sides.


12y=12 Combine like terms on the right side.


y=%2812%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=1 Reduce.


So the solutions are x=4 and y=1.


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 5x%2B3y=23 (red) and 2x%2B4y=12 (green)

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim