When solving ordinary – linear – simultaneous equations we multiply the equations by constant factors to make the coefficient of some variable the same in magnitude, then add or subtract the equations to eliminate that variable.
For example, solve
(1)
(2)
(1)*2-(2)*3 eliminates
to give
Substitution of this value ofinto (1) to find a gives
If one of the equations is a quadratic we may not be easily able to rearrange the equations to easily eliminate one of the variables and solve the equations. But we can rearrange one of the equations – usually the linear one - to make either
or
the subject.
Example:
(1)
(2)
Rearrange (1) to makethe subject:
and substitute this into (2) to get
To solve the last equation we can either factorise or use the quadratic formula.
By factorising:
or
If
from
If
from
By using the quadratic formula:
hence
or 3.
As before , substitute these values of
back into (1) to obtain