Systems of Equations & Inequalities Review

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 does it mean to solve a system of equations by graphing?

Back

To solve a system of equations by graphing means to plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Tags

CCSS.8.EE.C.8B

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Tags

CCSS.6.EE.B.8

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves shading the region of the graph that satisfies the inequality, using a solid line for 'greater than or equal to' and 'less than or equal to', and a dotted line for 'greater than' and 'less than'.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a solid line and a dotted line when graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dotted line indicates that points on the line are not included (> or <).

Tags

CCSS.HSA.REI.D.12

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives in the problem, then express them as inequalities using variables to represent the quantities involved.

Front

What is the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph that satisfies all the inequalities in the system, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines representing the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A