# Thread: Solving 2 equations with 1 variable

1. ## 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?

2. ## Re: Solving 2 equations with 1 variable

$12l - 0.75l^2 = 24l - 2.25l^2$

$1.5l^2 - 12l = 0$

$1.5l(l - 8) = 0$

$l = 0$ , $l = 8$

3. ## 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?

4. ## Re: Solving 2 equations with 1 variable

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

5. ## Re: Solving 2 equations with 1 variable

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

6. ## 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?

7. ## Re: Solving 2 equations with 1 variable

Do you know how to solve quadratic equations? As skeeter showed, with A= X, you have $12L- .75L^2= 24L- 2.25L^2$. Adding $2.25L^2$ to both sides and subtracting 24L from both sides, you get $1.5L^2- 12L= 0$. 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: $L(1.5L- 12)= 0$. 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.

8. ## 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!!