Solving Systems of Equations:
Previously, we have been dealing with just one equation at a time. But now, we will work with more than one variable and more than one equation. These are termed as systems of equations. Whenever answering a system of equations, you require giving the value for each and every variable.
Solving Systems of Linear Equations:
There are six ways that we can utilize to solve a system of the linear equations:
Gaussian Elimination/Gauss Jordan Elimination:
Matrix Algebra/Matrix Inverses:
The technique of substitution will work with non-linear and also linear equations.
a) Solve one of the equations for one of variables.b) Replace that expression in for the variable in other equation.c) Solve the equation for the residual variable.d) Back-substitute the value for variable to determine the other variable.e) Check.
The procedure of back-substitution includes taking the value of variable found in step c and replacing it back to the expression obtained in step a (or the original problem) to find out the remaining variable.
It is significant that both the variables be given whenever solving a system of equations. The common mistake students make is to find out one variable and stop there. You need to comprise a value for all variables.
This is a good idea to ensure your answer to the both equations, however is probably adequate to check the equation you did not isolate the variable in first step. That is, when you solved for y in the first equation in step a, employ the second equation to ensure the answer.
The graphical approach works fine with a graphing calculator, however is imprecise by hand (did such points intersect at 1/6 or 1/7?) unless the graph occurs to drop exactly on grid lines.
a) Solve each of equation for y. This might include a plus and minus when there is an y2 term. When you are not graphing with a computer or calculator, you can skip this step.
b) Graph each and every equation.
c) Find out the points of intersection.
It is significant to check your answers to make sure that you read the intersection point properly.
Sometimes the calculator will fail to provide an intersection point by using the intersect command. You might need to use the trace characteristic of the calculator to determine the intersection point. You might use your calculator to ensure the answer.
Try to transform your answer to fractional form when possible.
The graphical approach can keep a lot of time whenever you are working with the non-linear system of equations.
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