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Solving Systems of Linear Inequalities 11429 Views
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Description:
How do you solve a system of linear inequalities? Aw, man...and we thought solving a problem like Maria was tough...
- Mathematics and Statistics Assessment / Linear Equations, Inequalities, and Systems
- Algebra / Represent and solve equations and inequalities graphically
- Algebra / Represent and solve equations and inequalities graphically
- Algebra / Represent and solve equations and inequalities graphically
- Algebra / Represent and solve equations and inequalities graphically
Transcript
- 00:04
Solving Systems of Linear Inequalities, a la Shmoop.
- 00:09
Black Beard and his friend Red Beard are aspiring pirates.
- 00:13
In order to get their official pirate badges, they must complete one final test…
- 00:17
…and be the first team of two to find a treasure chest of gold.
- 00:22
Because they were one of the fastest teams at shipbuilding, they are given one special
Full Transcript
- 00:26
hint. y is greater than x plus 3, and y less than
- 00:31
or equal to negative 3/2 x plus 1. Thankfully, Black Beard paid attention in
- 00:37
math class… … and sees that the hint gives them a rough
- 00:40
idea of where on the map to find that treasure chest.
- 00:45
Let’s start by graphing the first line: y equals x plus 3.
- 00:53
The equation is in slope-intercept form, so we can plot 3 on the y-axis as the y-intercept.
- 01:05
The slope of the line is 1. We know that slope is rise over run, so we can rise 1 units on
- 01:11
the y-axis, and run over 1 unit to the right. Since the inequality doesn’t include equals
- 01:18
to, we know the line will be dotted and not solid.
- 01:22
To see which side of the line we should shade for the inequality, we can test a point on
- 01:28
one side of the line. For example…(0, 4) If we plug in 0 for x,
- 01:35
we get that 0 plus 3 is 3. Since our point’s y-value of 4 is greater
- 01:41
than 3, we know that we can shade the upper half of the line.
- 01:47
For the second line, we have y is less than or equal to negative 3/2 x plus 1, so we can
- 01:59
graph y equals to negative 3/2 x plus 1 first. The equation is in slope-intercept form, so
- 02:07
we can plot 1 on the y-axis as the y-intercept. The slope of the line is -3/2. We know that
- 02:16
slope is rise over run, so we can go down 3 units on the y-axis, and run over 2 units
- 02:22
to the right. Since the inequality includes equals to, we
- 02:26
know the line will be solid. To see which side of the line we should shade
- 02:31
for the inequality, we can test a point on one side of the line.
- 02:36
For example…(-2, 0). If we plug in -2 for x, we get that negative 3/2 times -2 equals
- 02:46
3…3 plus 1 is 4. Since our original y-value of 0 is less than
- 02:53
4, we know we can shade the lower half of the line.
- 02:58
Seeing where the two shaded regions intersect, we get our solution.
- 03:02
Now Black Beard and Red Beard know where to start looking for that treasure.
- 03:06
Hopefully they can track it down before they’re both White Beard.
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