Thanks for your help with the solving of the three equations! Yes, it was a typo. I just finished solving it a long way, solving for the 1st 2 equations then the 2nd and 3rd and plugging in variables...etc. etc. Your way gave the same answer, but quicker, does your way always work???
if there is a solution, it works
the method I used is "elimination"
you have to look for the variable with the "easiest" number combination
It was luck that in the second set of equations we had 5x in both, that made it easy to simply subtract them.
Had the coefficients been different you would have to multiply by suitable numbers to get them the same.
thanks for the clarification!!
You're welcome! I'm glad I could help you solve the equations. To answer your question, my method of solving equations is based on concepts and techniques that always work for linear equations. Linear equations are equations in which the highest power of the variable is 1.
The method I use is called the "simultaneous equations" or "system of equations" method. This method involves solving multiple equations simultaneously to find the values of the variables that satisfy all the given equations.
In the case of three linear equations, we can use various techniques like substitution, elimination, or matrix methods to solve them. The specific technique depends on the equations and can vary from problem to problem.
However, if all the given equations are linear and solvable, the simultaneous equations method is guaranteed to find the solution. It may not always be the quickest method, as the complexity of the equations can vary, but it ensures a systematic approach to finding the solution.
It's always a good idea to check your answer by plugging the values of the variables back into the equations to make sure they satisfy all the given equations.