Well, the definition of a system of linear equations is: Any equation that can be written in the form Ax + By = C. Where A, B, & C are real numbers. A and B can not both be zero (0). The System of equations is a set of equations with the same variables is a system of equations.
1. Must have 1 or 2 variables "x,y, etc.".
2. Variables cannot have exponts other than 1.
3. Variables cannot be in the denominator unless it's a single variable equation.
4. Variables cannot be multiplied together. "X * Y = xy".
The three types of systems are 1. Consistent and independent, 2. Consistent and dependent, and 3. Inconsistent. You will know that it is consistent and independent when the lines on the graph of the equation intersect, the slopes of the lines are different, and the number of solutions are 1. The 2nd is consistent and dependent. The lines on this graph coincide. The slope of this one is the same and the intercepts are the same. The number of solutions for this one is infinite cause everything is the same. The 3rd and last one is inconsistent. The lines on this graph are parallel. It has the same slope, but different intercepts. But at the same time it has no solutions, none.
The elimination method, substitution method, and cramer's rule and 3 ways to solve an .
equations algebraically. With the elimination method you arrange both equations into standard form with like terms over each other. Then you pick a variable to elininate. Arrange so that the coefficients of .
that variable are opposites of one another. Add the equations, leave one equation with one of the .
variable, then just solve the rest of the problem.
The substitution method is kinda the same but not really. 1st you solve for one of the variables. Then in the other equation, you substitute for the the variable you just solved. Solve the newer .
equation, then substitute the value found into any equation involving both variables and solve for the other variable.