# Solving Systems of Linear Inequalities

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How do you solve a system of linear inequalities? Aw, man...and we thought solving a problem like Maria was tough...

Algebra | Represent and solve equations and inequalities graphically Systems of Equations |

Language | English Language |

Mathematics and Statistics Assessment | Linear Equations, Inequalities, and Systems |

### Transcript

hint. y is greater than x plus 3, and y less than

or equal to negative 3/2 x plus 1. Thankfully, Black Beard paid attention in

math class… … and sees that the hint gives them a rough

idea of where on the map to find that treasure chest.

Let’s start by graphing the first line: y equals x plus 3.

The equation is in slope-intercept form, so we can plot 3 on the y-axis as the y-intercept.

The slope of the line is 1. We know that slope is rise over run, so we can rise 1 units on

the y-axis, and run over 1 unit to the right. Since the inequality doesn’t include equals

to, we know the line will be dotted and not solid.

To see which side of the line we should shade for the inequality, we can test a point on

one side of the line. For example…(0, 4) If we plug in 0 for x,

we get that 0 plus 3 is 3. Since our point’s y-value of 4 is greater

than 3, we know that we can shade the upper half of the line.

For the second line, we have y is less than or equal to negative 3/2 x plus 1, so we can

graph y equals to negative 3/2 x plus 1 first. The equation is in slope-intercept form, so

we can plot 1 on the y-axis as the y-intercept. The slope of the line is -3/2. We know that

slope is rise over run, so we can go down 3 units on the y-axis, and run over 2 units

to the right. Since the inequality includes equals to, we

know the line will be solid. To see which side of the line we should shade

for the inequality, we can test a point on one side of the line.

For example…(-2, 0). If we plug in -2 for x, we get that negative 3/2 times -2 equals

3…3 plus 1 is 4. Since our original y-value of 0 is less than

4, we know we can shade the lower half of the line.

Seeing where the two shaded regions intersect, we get our solution.

Now Black Beard and Red Beard know where to start looking for that treasure.

Hopefully they can track it down before they’re both White Beard.