Systems of Equations and Inequalities Quick Check

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

Tags

CCSS.HSA.REI.D.12

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution of a system of equations represent?

Back

The solution of a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two lines coincide in a system of equations?

Back

If two lines coincide, it means they are the same line, indicating that the system has infinitely many solutions.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines: 1. Different slopes = one solution. 2. Same slope, different intercepts = no solution. 3. Same slope, same intercept = infinitely many solutions.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the inequality y < 2x - 4?

Back

The graphical representation is a dashed line for y = 2x - 4, with the area below the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the coordinate plane into two regions, indicating where the inequality holds true (shaded region) and where it does not (unshaded region).

Tags

CCSS.HSA.REI.D.12

Front

How do you write inequalities from a word problem?

Back

Identify the variables, determine the constraints, and express them as inequalities based on the relationships described in the problem.

Tags

CCSS.6.EE.B.8