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.

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by 4.

Distribute and multiply.

Multiply the both sides of the second equation by -3.

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.

Subtract from 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)

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

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