2. Definitions System – a conjunction of two or more equations GENERAL FORM: Solution – an ordered pair of values that will satisfy all equations in the system
3. Solution of Two Variable System Assigning 2 points for each line Computing the intercepts of each line Converting each line into y=mx + b
4. Solution of Two Variable System Isolating one variable Eliminating one variable and solving the other Solving for the determinants
5. Graphical Method Only intersecting equations have a unique or finite solution. They are called consistent equations. However, there are also systems that has infinite solutions or no solutions at all. Inconsistent equations – if two lines are parallel, then the system has no solution
13. Algebraic Solution Elimination Method (Gaussian Elimination) Find equations equivalent to the two given equations such that the coefficients of one variable are additive inverse or the same By addition or subtraction of the two equations, we eliminate one variable Derive a linear equation in one variable and solve that variable Substitute the value of the solved variable in the other equation and solve for the second variable
23. Three Variable System To determine the solution to a system of 3 variables, we can use either Elimination or Cramer’s Rule
24. Elimination: 3 Variable System Equation 1 2 VAR SYSTEM Equation 4 VAR 1 Value of VAR 3 Equation 2 VAR 2 Equation 5 VAR 1 Equation 3 Apply Back Substitution