MATH 416Equations & 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 situationSSolution (2,1)

Graphing Systems of Equations

Solving systems of equations with graphic method:

_Easy situation

x y2 44 66 88 10

x y2 26 88 1210 16

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 1.6Ex 1.2, Page 1.13

Graphing Systems of Equations

Solving systems of equations (Special cases):

When both y1 = m1x + n1 & y2 = m2x + n2 expressions have the same slope (m1 = m2), but

different constant term (n1≠ n2), 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 1.15

2x - y = -52x - y = 3

Graphing Systems of Equations

Solving systems of equations (Special cases):

When both y1 = m1x + n1 & y2 = m2x + n2 expressions have the same slope (m1 = m2), and the same constant term (n1= n2), 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(Special cases):Example 2, Page 1.17

+ = 1x + = 2

Graphing Systems of Equations

Solving systems of equations with graphic method:

Practice Ex 1.2, Page 1.20