REVIEW Systems of Linear Equations & Inequalities12.12.24

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system has infinitely many solutions?

Back

It means that there are countless pairs of values that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the boundary line, indicating all the solutions.

Tags

CCSS.HSA.REI.D.12

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 all inequalities are satisfied, the point is a solution.

Front

What does the symbol '≤' represent in inequalities?

Back

It means 'less than or equal to'.

Tags

CCSS.6.EE.B.8

Front

What is the difference between 'no solutions' and 'one solution' in a system of equations?

Back

'No solutions' means the lines are parallel and never intersect; 'one solution' means the lines intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

How can you identify the solution set of a system of inequalities graphically?

Back

By shading the region where the inequalities overlap on the graph.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality 'y > 3x' represent graphically?

Back

It represents the area above the line y = 3x, not including the line itself.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the boundary line in a linear inequality?

Back

It separates the solution set from the non-solution set; whether it is included depends on the inequality symbol.

Tags

CCSS.HSA.REI.D.12

Front

How do you solve a system of linear equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6