1. MATH 416 Equations & Inequalities II

2. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates of the point that common to the two lines (intersection point).

3. Graphing Systems of Equations Solving systems of equations with graphic method: _Easiest situation S Solution (2,1)

4. Graphing Systems of Equations Solving systems of equations with graphic method: _Easy situation xy 24 46 68 810 xy 22 68 812 1016 Solution (6,8)

5. Graphing Systems of Equations Solving systems of equations with graphic method: _Transform both lines to the y = mx + n form _Obtain set of solution pairs (x, y) for each line *If no solution pair (x, y) is repeated in both sets, then… _Plot both sets of solution pairs into a graph _Determine the coordinates of the intersection point (solution)

6. Graphing Systems of Equations Solving systems of equations with graphic method: Practice Ex 1.1, Page 1.6 Ex 1.2, Page 1.13

7. Graphing Systems of Equations Solving systems of equations (Special cases): When both y 1 = m 1 x + n 1 & y 2 = m 2 x + n 2 expressions have the same slope (m 1 = m 2 ), but different constant term (n 1 ≠ n 2 ), the lines obtained are parallel and the system has no solution *Could occur with any of the four methods for solving equations

8. Graphing Systems of Equations Solving systems of equations with graphic method (Special cases): Example 1, Page 1.15 2x - y = -5 2x - y = 3

9. Graphing Systems of Equations Solving systems of equations (Special cases): When both y 1 = m 1 x + n 1 & y 2 = m 2 x + n 2 expressions have the same slope (m 1 = m 2 ), and the same constant term (n 1 = n 2 ), the lines obtained are identical and the system has infinite solutions *Could occur with any of the four methods for solving equations

10. Graphing Systems of Equations

11. Solving systems of equations with graphic method : Practice Ex 1.2, Page 1.20