Section 3.1 and 3.2 Systems of Equations A system of equations is a set of two or more equations containing two or more variables. A linear system is a system of equations containing only linear equations. On the graph of the system of two equations, the solution is the set of points where the lines intersect. Two methods for solving algebraically: Substitution and Elimination Example #1: Solve the system using substitution. y+2=
2xx – 3y = 3 You Try: Use substitution to solve: 2y + x = 4 3x – 4y = 7 Section 3.1 and 3.2 Example #2: Use elimination method to solve the system. 3x + 2y = 4 4x – 2y = –18 You try: Section 3.1 and 3.2 Three-­‐Variables: Systems of three equations with three variables are often called 3-­‐
by-­‐3 systems. In general, to find a single solution to any system of equations, you need as many equations as you have variables. Example #1: Step 1 Eliminate one variable. Step 2 Eliminate another variable. Then solve for the remaining variables using your knowledge of 2 variable systems. Section 3.1 and 3.2 Example #2: