Solving Simultaneous Equations: Write s In Terms Of a Only

Question

For each of the following pairs of equations, write s in terms of a only:

3s−ah=a²
as+2h=3a

Show that s=5a²/a²+6

Answer 1

3s−ah=a²
as+2h=3a

 

From equation 1:

ah = 3s  - a²

h = (3s-a²)/a

 

plugging into equation 2

as + 2[(3s-a²)/a] = 3a

 

as + (6s-3a²)/a = 3a

a²s + 6s - 3a² = 3a²

s(a² + 6) - 3a² = 3a²

s(a² + 6) = 6a²

 

s = 6a²/(a²+6)

 

Answer 2

 

First equation:

 

3s = a^2 + ah

 

s = (a^2 + ah)/3

 

 

Second equation:

 

as = 3a - 2h

 

s = (3a - 2h)/a