MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a...
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Transcript of MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a...
![Page 1: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/1.jpg)
MATH 416Equations & Inequalities II
![Page 2: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/2.jpg)
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).
![Page 3: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/3.jpg)
Graphing Systems of Equations
Solving systems of equations with graphic method:
_Easiest situationSSolution (2,1)
![Page 4: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/4.jpg)
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)
![Page 5: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/5.jpg)
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)
![Page 6: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/6.jpg)
Graphing Systems of Equations
Solving systems of equations with graphic method:
Practice Ex 1.1, Page 1.6Ex 1.2, Page 1.13
![Page 7: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/7.jpg)
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
![Page 8: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/8.jpg)
Graphing Systems of Equations
Solving systems of equations with graphic method(Special cases):Example 1, Page 1.15
2x - y = -52x - y = 3
![Page 9: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/9.jpg)
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
![Page 10: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/10.jpg)
Graphing Systems of Equations
Solving systems of equations with graphic method(Special cases):Example 2, Page 1.17
+ = 1x + = 2
![Page 11: MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.](https://reader036.fdocuments.in/reader036/viewer/2022082601/5a4d1b507f8b9ab0599a734b/html5/thumbnails/11.jpg)
Graphing Systems of Equations
Solving systems of equations with graphic method:
Practice Ex 1.2, Page 1.20