How do you find the solution of the system of equations #8x^2 + 5y =100# and #6x^2 -x -3y =5#?
1 Answer
The most straight forward (but not always the best) way to solve any system of equations is the method of substitution. In short, the way to do it is to find a simplest equation, from which you can represent a value of one of the variables in terms of all others, and substitute this into all other equations, thus reducing the number of equations and the number of variables. Then do it again and again until you are left with only one equation with one variable.
Let's apply this to our system. It looks like we can easily represent
Now substitute it into the second equation getting
The latter is a simple quadratic equation with one variable
Solutions to this equations are
or
Now we can return to our representation of
So, we have two solutions to our system of equations:
Always check the solutions.
Check 1. Substituting
Both equations check.
Check 2. Substituting
Both equations check.