MATH 416 Equations & Inequalities II

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).

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

Graphing Systems of Equations Solving systems of equations with graphic method: _Easy situation xy xy Solution (6,8)

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)

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

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

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

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

Graphing Systems of Equations

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