How do you convert the equation $$5y - x = 5$$ to slope-intercept form?

To convert to slope-intercept form, solve for $$y$$ : 1. Add $$x$$ to both sides: $$5y = x + 5$$ . 2. Divide by 5: $$y = \frac{1}{5}x + 1$$ .

What is the graphical representation of the inequality $$y \ge \frac{3}{4}x - 2$$ ?

The graph includes the line $$y = \frac{3}{4}x - 2$$ with a solid line, shading above the line to indicate all points where $$y$$ is greater than or equal to the line.

What does the inequality $$y

The graph includes the line $$y = -\frac{1}{3}x + 2$$ with a dashed line, shading below the line to indicate all points where $$y$$ is less than the line.

What is the difference between intersecting lines and parallel lines in a system of equations?

Intersecting lines have one solution (the point of intersection), while parallel lines have no solutions as they never meet.

How can you graph a system of inequalities?

Graph each inequality as a line, use solid or dashed lines as appropriate, and shade the region that satisfies each inequality.

What is the meaning of the term 'solution set' in the context of inequalities?

The solution set is the collection of all points that satisfy the given inequalities, represented graphically as a shaded region.

What does it mean for a system of equations to be consistent?

A consistent system has at least one solution, which can be either a single point (intersecting lines) or infinitely many solutions (coincident lines).

What is the role of the slope in a linear equation?

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

How do you identify the feasible region in a system of inequalities?

The feasible region is the area where the shaded regions of all inequalities overlap, representing all possible solutions.

What is the graphical representation of the solution to the system of inequalities $$y \ge \frac{3}{4}x - 2$$ and $$y

The solution is the area where the shaded regions of both inequalities overlap, bounded by the lines.

Chapter 6 Review - Solving Systems with Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is slope-intercept form?

Back

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

3.

FLASHCARD QUESTION

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the graphs of the equations are parallel lines, meaning they never intersect.

Tags

CCSS.8.EE.C.8A

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.D.12

5.

FLASHCARD QUESTION

Front

What is the solution to the system of equations represented by the point (1, 3)?

Back

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

6.

FLASHCARD QUESTION

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

7.

FLASHCARD QUESTION

Front

What is the significance of the y-intercept in a linear equation?

Back

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