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# System Of Inequalities

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#### Transcript of System Of Inequalities

How it Works 0 + - = 9 8 7 1 2 3 4 5 6 c Problem #1 Problem #2 x – y < –2

x – y > 2 Any Questions? A "system" of linear inequalities is a set of linear inequalities that you deal with all at once.

Usually two or three linear inequalities. 1.Solve for "y"

2.Graph each Inequality

3.Find the solution by the shaded region. Steps for Solving

the

Systems of Inequalities Rules! Graphs Type of Solution This kind of solution is called "unbounded", because it continues forever in at least one direction

In this case, forever downward. Work Cited Systems OF Inequalities. What are System of Inequalities? 1.If the inequality is < or > a dotted line must be used to represent the line.

2.If the inequality is < or >, a solid line is used.

3.Choose a test point to determine which side of the line needs to be shaded.

4.The solution, S, is where the two shadings overlap one another. 2x – 3y < 12

x + 5y < 20

x > 0 Step #1: Solve for "y". 2x – 3y < 12

x + 5y < 20

x > 0 y > ( 2/3 )x – 4

y < ( – 1/5 )x + 4

x > 0 "Solving" systems of linear inequalities means:

"graphing each individual inequality, and then finding the overlaps of the various solutions".

So I graph each inequality, and then find the overlapping portions of the solution regions. Step #2: Graph FIRST Inequality y > ( 2/3 )x – 4 Continued. . . This inequality is a "greater than" inequality, so I want to shade above the line.

However. since there will be more than one inequality on this graph, I don't know (yet) how much of that upper side I will actually need. Step #3: Graph SECOND Inequality y < (-1/5 )x + 4 Continued. . . Since this is a "less than" inequality, I'll draw the fringe along the bottom of the line Step #4: Graph THIRD Inequality The line "x = 0" is just the y-axis, and I want the right-hand side.

I need to remember to dash the line in, because this isn't an "or equal to" inequality,

So the boundary (the line) isn't included in the solution. Continued. . . The "solution" of the system is the region where all three individual solution regions overlap.

In this case, the solution is the shaded part in the middle. TYPE OF SOLUTION The solution region for this called a "closed" or "bounded" solution, because there are lines on all sides.

That is, the solution region is a bounded geometric figure (a triangle, in that case). PROBLEM #2 2x - y> -3

4x + y < 5 Solve for "y". 2x - y> -3

4x + y < 5 y < 2x + 3

y < -4x + 5 Graph FIRST Inequality y < 2x + 3 Graph SECOND Inequality

y < -4x + 5 Finding Solution The solution is the lower region, where the two individual solutions overlap. Type Of Solution But there is no place where the individual solutions overlap.

Note that the lines y=x+2 & y=x–2 never intersect,being parallel lines with different y-intercepts.

Since there is no intersection, there is no solution. Graph SECOND Inequality y < x – 2 Graph FIRST Inequality y > x + 2 Solve for "y". x – y < –2

x – y > 2 y > x + 2

y < x – 2 http://www.purplemath.com/modules/syslneq.htm

http://www.regentsprep.org/Regents/math/ALGEBRA/AE9/GrIneq.htm http://www.freemathhelp.com/systems-inequalities.html

Full transcriptx – y > 2 Any Questions? A "system" of linear inequalities is a set of linear inequalities that you deal with all at once.

Usually two or three linear inequalities. 1.Solve for "y"

2.Graph each Inequality

3.Find the solution by the shaded region. Steps for Solving

the

Systems of Inequalities Rules! Graphs Type of Solution This kind of solution is called "unbounded", because it continues forever in at least one direction

In this case, forever downward. Work Cited Systems OF Inequalities. What are System of Inequalities? 1.If the inequality is < or > a dotted line must be used to represent the line.

2.If the inequality is < or >, a solid line is used.

3.Choose a test point to determine which side of the line needs to be shaded.

4.The solution, S, is where the two shadings overlap one another. 2x – 3y < 12

x + 5y < 20

x > 0 Step #1: Solve for "y". 2x – 3y < 12

x + 5y < 20

x > 0 y > ( 2/3 )x – 4

y < ( – 1/5 )x + 4

x > 0 "Solving" systems of linear inequalities means:

"graphing each individual inequality, and then finding the overlaps of the various solutions".

So I graph each inequality, and then find the overlapping portions of the solution regions. Step #2: Graph FIRST Inequality y > ( 2/3 )x – 4 Continued. . . This inequality is a "greater than" inequality, so I want to shade above the line.

However. since there will be more than one inequality on this graph, I don't know (yet) how much of that upper side I will actually need. Step #3: Graph SECOND Inequality y < (-1/5 )x + 4 Continued. . . Since this is a "less than" inequality, I'll draw the fringe along the bottom of the line Step #4: Graph THIRD Inequality The line "x = 0" is just the y-axis, and I want the right-hand side.

I need to remember to dash the line in, because this isn't an "or equal to" inequality,

So the boundary (the line) isn't included in the solution. Continued. . . The "solution" of the system is the region where all three individual solution regions overlap.

In this case, the solution is the shaded part in the middle. TYPE OF SOLUTION The solution region for this called a "closed" or "bounded" solution, because there are lines on all sides.

That is, the solution region is a bounded geometric figure (a triangle, in that case). PROBLEM #2 2x - y> -3

4x + y < 5 Solve for "y". 2x - y> -3

4x + y < 5 y < 2x + 3

y < -4x + 5 Graph FIRST Inequality y < 2x + 3 Graph SECOND Inequality

y < -4x + 5 Finding Solution The solution is the lower region, where the two individual solutions overlap. Type Of Solution But there is no place where the individual solutions overlap.

Note that the lines y=x+2 & y=x–2 never intersect,being parallel lines with different y-intercepts.

Since there is no intersection, there is no solution. Graph SECOND Inequality y < x – 2 Graph FIRST Inequality y > x + 2 Solve for "y". x – y < –2

x – y > 2 y > x + 2

y < x – 2 http://www.purplemath.com/modules/syslneq.htm

http://www.regentsprep.org/Regents/math/ALGEBRA/AE9/GrIneq.htm http://www.freemathhelp.com/systems-inequalities.html