2l+2w=22
(1/2)l+w+5=12
(please show work because I DONT UNDERSTAND IT)

Question

mathteacher1729 · Answer

This is a "system of two equations in two unknowns"

Let's begin by replacing: 
the letter L with X
the letter W with Y
The two equations are now:

$$2x +2y =22$$
$$\frac{1}{2}x +y+5=12$$

Ultimately this represents two straight lines which may do one of three things:

1) They will overlap (they are the same line)
2) They will intersect at exactly one point. (the solution)
3) They will be parallel and will NEVER intersect (there is no solution)

Let's begin by taking

$$2x +2y =22$$

and dividing everything by 2

$$x +y =11$$

We'll leave that alone for a second...

Now let's take

$$\frac{1}{2}x +y+5=12$$

and get rid of the fraction by multiplying everything by 2

$$x +2y+10=24$$

Let's subtract 10 from both sides now:

$$x +2y=14$$

Ok!  So now we have a much easier "system of linear equations" to deal with. :)

We can subtract the top equation from the bottom equation to "eliminate x"

$$x +2y=14$$
$$-(x +y =11)$$

IMPORTANT -- remember to distribute that negative!
And this will give us:

$$x +2y=14$$
$$-x-y=-11$$

Now that x is gone we have:

$$y=3$$

So we are almost done! :)

Now take y = 3 and "Substitute" it into x + y = 11

$$x + 3 = 11$$

subtract 3 from both sides:

$$x = 8$$

So the final solution is

$$(3,8)$$

TEST THIS OUT!!!

Get your calculator and graph:

$$y_1=11-x$$
$$y_2=7-\frac{1}{2}x$$

You will see that they intersect EXACTLY at (3,8).

Hope this helps! :)

anonymous · Answer

thank you :) i appreciate it... my 8th grade algebra teacher is not very good at helping me :) oh my gosh your a life saver.

mathteacher1729 · Answer

You're welcome. :)  Do you know how to graph this and test the intersection point?

anonymous · Answer

yes i pretty sure my graphing calculator with do that for me :)

mathteacher1729 · Answer

Well, yes, the graphing calculator can graph it, but do you know how to enter in y1 and y2, etc. ? :p

anonymous · Answer

O ya .That was on my last quiz. I learned that last week. Im pretty smart when it comes to technology and learning how to use it.\

mathteacher1729 · Answer

Awesome! :) I don't know if you have heard of GeoGebra but it is an AWESOME piece of graphing software. http://www.geogebra.org/cms/en/installers Give it a try!

anonymous · Answer

thanks i will definitely download that sometime :)