How do you solve the following system?: #-8x -6y =3, -2x +3y = -7#
Isolate one variable via adding/subtracting the equations and determine its value, then substitute that back into the equations to determine the other variable.
When confronted with a system of equations that consists of an equal number of variables and equations, it behooves us to attempt to manipulate the equations such that we can isolate and determine the value of one of the variables, which normally allows us to substitute that value for the variable in the equation.
In this case, our system of equations consists of:
Now our manipulation begins. How can we add or subtract multiples of
From examining the equation, we determine there are two (well, technically 3) ways to do this:
Note that 1 and 2 are essentially the same operation, simply reordered.
Although above we have already determined the solution (e.g.
We might prefer operation
The solution we have obtained is
If we wish, then at this point we may substitute the values for
The solution checks out.