Question

a + b + c = 3.03
4a + 2b + c = 1.72
9a + 3b = c = 1.17
Help me to solve these simultaneous equations

Answer 1

Let the equation be : at^2 + bt + c = P, where t = time (hrs), P = population (1000's).

When t = 1, P = 3.03.
When t = 2, P = 1.72.
When t = 3, P = 1.17.

Substitute these into the equation to obtain these 3 simultaneous equations :

a + b + c = 3.03
4a + 2b + c = 1.72
9a + 3b = c = 1.17

Solving gives : a = 0.38, b = -2.45, c = 5.1.

The equation is therefore, P = 0.38t^2 - 2.45t + 5.1

Testing with t = 0 to 6 gives the population values as provided,
so it seems to be a valid model.

At t = 9 hrs, P = 0.38*9^2 - 2.45*9 + 5.1 = 13.83.

Answer 2

you know, c = 1.17
put in equation 1 and 2 and solve those two equations simultaneoulsy to get a and b.

Answer 3

@Beast-Mode: Are you sure that your input is relevant to the question posted?
In your shoes I'd present and discuss several different methods for solving a system of 3 linear equations.

Answer 4

@Arihangdu: Which such methods have y ou heard about up to now?

Answer 5

Arihangdu
a + b + c = 3.03
4a + 2b + c = 1.72
9a + 3b = c = 1.17
Help me to solve these simultaneous equations.
(You say you know the elimination and substitution methods.)

Let's eliminate the variable " a " ... please multiply the first equation (all of it) by -4.

Combine this new version of the first equation with the second equation as-is:

-4a - 4b - 4c = -4(3.03)
+4a +2b + c = 1.72
----------------------
This eliminates " a " from the 2nd equation.

Next, mult. the 1st eq'n by -9. (Why?)
Combine the resulting equation with the 3rd given equation.

Please show your work. Will be happy to comment further after we hear back from you.

Answer 6

This method is also called the "addition and subtraction method," which is used to eliminate variables. You could eliminate variable a, then eliminate variable b, leaving you with only variable c, which you can now find.