# Write a system of linear equations for the shaded region

### Graphical representation of linear inequalities

The graph of the system is the intersection of the shaded regions for each inequality in the system. Provided by: Monterey Institute of Technology. So, the shaded area shows all of the solutions for this inequality. Her morning cereal satisfies some of her calcium requirements, but she needs an additional milligrams of calcium, which she will get from a combination of broccoli, at milligrams per serving, and zucchini, at 30 milligrams per serving. Graphing two-variable linear inequalities Video transcript We're asked to determine the solution set of this system, and we actually have three inequalities right here. Checking points M and N yield true statements. The following example shows how to test a point to see whether it is a solution to a system of inequalities. If the inequality is strict, make the boundary line a dashed line. To create a system of inequalities, you need to graph two or more inequalities together.

We will verify algebraically whether a point is a solution to a linear equation or inequality. In this case, it is shown as a dashed line as the points on the line do not satisfy the inequality. The student is expected to: A 3 D graph the solution set of linear inequalities in two variables on the coordinate plane Resource Objective s The student will construct the graph of a one-variable or two-variable inequality and find its solution.

Checkpoint 8. For any x, this is 2x minus 5, and we care about the y's that are less than that.

The boundary line divides the coordinate plane in half. So the y-intercept right here is 1.

## Writing inequalities from graphs

Journal Activity Let's Get Started We're going to learn how to graphically find the solution to one-variable and two-variable inequalities. But as you can see, their solutions sets are completely non-overlapping. So let's first graph y is equal to 2x plus 1, and that includes this line, and then it's all the points greater than that as well. If we move forward 2, we'll move up 4, just like that. Provided by: Monterey Institute of Technology. If your inequality symbol is "less than" or "less than or equal to," where is your solution region? You will also review how to convert a linear equation from standard form to slope-intercept form.

So this graph is going to look something like this. The line is dashed as points on the line are not true.

If x is 0, y is 1, and the slope is 2. So there is actually no solution set.

You will also review how to convert a linear equation from standard form to slope-intercept form. Here is a summary of our test point method for graphing inequalities.

Substitute the coordinates of the test point into the inequality.

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