# Solving 2 equations with 1 variable

• Jul 10th 2012, 01:37 PM
snypeshow
Solving 2 equations with 1 variable
I'm having trouble with this. i know it's simple, but I'm honestly blanking out on how to do this:

2 equations:

X = 12L - 0.75L^2
A = 24L - 2.25L^2

What does L equal when X and A intersect?

I know this means when X = A, which is 12L - 0.75L^2 = 24L - 2.25L^2

The answer is X = A at 8 but how do I find this?
• Jul 10th 2012, 01:44 PM
skeeter
Re: Solving 2 equations with 1 variable
\$\displaystyle 12l - 0.75l^2 = 24l - 2.25l^2\$

\$\displaystyle 1.5l^2 - 12l = 0\$

\$\displaystyle 1.5l(l - 8) = 0\$

\$\displaystyle l = 0\$ , \$\displaystyle l = 8\$
• Jul 10th 2012, 01:52 PM
snypeshow
Re: Solving 2 equations with 1 variable
I understand what you did up to the third line, could you explain that?

did you do 12/1.5 to get 8?
• Jul 10th 2012, 01:56 PM
snypeshow
Re: Solving 2 equations with 1 variable
Oh okay, I get it!! You factored the second part. but where do you find L = 100?
• Jul 10th 2012, 02:15 PM
skeeter
Re: Solving 2 equations with 1 variable
Quote:

Originally Posted by snypeshow
Oh okay, I get it!! You factored the second part. but where do you find L = 100?

L = 0 , not 100
• Jul 10th 2012, 02:24 PM
snypeshow
Re: Solving 2 equations with 1 variable
Sorry about that (I was trying to apply what you did two another exercise), I meant: Where do you find L = 8?
• Jul 10th 2012, 02:50 PM
HallsofIvy
Re: Solving 2 equations with 1 variable
Do you know how to solve quadratic equations? As skeeter showed, with A= X, you have \$\displaystyle 12L- .75L^2= 24L- 2.25L^2\$. Adding \$\displaystyle 2.25L^2\$ to both sides and subtracting 24L from both sides, you get \$\displaystyle 1.5L^2- 12L= 0\$. The simplest way to solve a quadratic equation is to factor (if you can). Here, we can see there is an "L" in both parts so we can factor that out: \$\displaystyle L(1.5L- 12)= 0\$. The crucial arithmetic point here is that if ab= 0, then either a= 0, or b= 0, or both. If the first factor, L, is 0, then, of course, we get the solution L= 0. If the other factor, 1.5L- 12= 0, we have 1.5L= 12 and then L= 12/1.5. 1.5 is, of course, the same as 3/2 and dividing by 3/2 is the same as multiplying by 2/3: = 12(2/3)= 24/3= 8.
• Jul 10th 2012, 02:54 PM
snypeshow
Re: Solving 2 equations with 1 variable
I know how to solve quadratic equations, but yeah, I never thought of solving it through factoring!! Thanks for the explanation HallsofIvy!!