How to determine the solution of a system of linear inequalities by graphing

The video tutorial explains how to solve and graph a linear system of inequalities. It begins by introducing the concept of graphing inequalities and rewriting them in slope-intercept form. The tutorial then demonstrates how to graph each inequality, identify parallel lines, and determine the appropriate shading regions using test points. The process involves plotting y-intercepts, using slopes to find additional points, and deciding whether boundary lines should be dashed or solid based on the inequality symbols. The tutorial concludes by showing how to identify the region that satisfies both inequalities.

What is the first step in graphing a system of linear inequalities?

• Find the intersection point.

• Shade the region above the line.

• Convert to standard form.

• Graph the boundary lines as equations.

How do you convert an inequality into slope-intercept form?

• Multiply both sides by the slope.

• Subtract the x-term from both sides.

• Add the y-intercept to both sides.

• Divide by the coefficient of y.

What does a dashed boundary line indicate in a graph of inequalities?

• The inequality is strictly greater than or less than.

• The inequality is less than or equal to.

• The inequality has no solution.

• The inequality is greater than or equal to.

If two lines have the same slope, what can be inferred about them?

• They form a right angle.

• They intersect at the origin.

• They are parallel.

• They are perpendicular.

What is the best test point to use when determining the shading region?

• (2,2)

• (-1,-1)

• (0,0)

• (1,1)

What does it mean if a test point satisfies an inequality?

• The point is irrelevant to the solution.

• The point is within the solution region.

• The point is outside the solution region.

• The point lies on the boundary line.

Where is the solution region located for a system of inequalities with parallel lines?

• Between the two lines.

• Below both lines.

• Above both lines.

• Outside the two lines.