Thread: 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?

,

I understand what you did up to the third line, could you explain that?

did you do 12/1.5 to get 8?

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

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

Sorry about that (I was trying to apply what you did two another exercise), I meant: Where do you find L = 8?

Do you know how to solve quadratic equations? As skeeter showed, with A= X, you have . Adding to both sides and subtracting 24L from both sides, you get . 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: . 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.

I know how to solve quadratic equations, but yeah, I never thought of solving it through factoring!! Thanks for the explanation HallsofIvy!!