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Hi, I'm Miss Davies.

In this lesson, we're going to be shading a region that has been defined by several inequalities.

We're going to find the region that satisfies both these inequalities.

We have here coordinate A which is 2,4.

We can say that y is greater than x-1 but the x-coordinate is not less than or equal to one.

With coordinate B, y is not more than x-1 and x is not less than not equal to one.

With coordinate C, which is 0, negative 3, y is not greater than x-1 but the x-coordinate is less than or equal to one.

With coordinate D, which is point 0,0, the y-coordinate is greater than x-1 and the x-coordinate is less than or equal to one.

This means that this is the region that satisfies both of these inequalities, meaning we can shade this area in.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The shaded region needs to be below y is equal to 1/2x + 1 and right of x equal two.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished Here is the answer.

The shaded region is below y is equal to negative x + 3 and below y is equal to two.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The shaded region needs to be above y is equal to negative x + 2 and below y is equal to 2x + 1.

We are going to shade the region that satisfies the three inequalities given.

If we look at the inequality, 2y is less than or equal to 3x-2.

We need to write this with y as the subject so you're going to divide both sides by two.

This gives us the inequality y is less than or equal to 3/2x-1.

We can then draw this line onto our coordinate grid.

It is a solid line as the inequality symbol is less than or equal two.

With our next inequality, it will be a dashed line through the point y is equal to negative 3.

Our final inequality will again be a dashed line that goes through x equals 2.

The region that satisfies all of these inequalities is here.

Within this, the y-coordinates are less than or equal to 3/2 x-1, the y-coordinates are greater than negative 3 and the x-coordinates are less than 2.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The shaded region needs to be above y is equal to negative 6x + 8 and below y is equal to 8 and right of x is equal to 1.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The first inequality can be rearranged to y is greater than negative x + 2.

The shaded region is above this, below y is equal to x and left of x is equal to 4.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The shaded region is above y is equal to negative 4x, above y is equal to 2x-4, and below zero is equal to x + y or y is equal to negative x.

That's all for this lesson.

Thanks for watching.