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.

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.

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.

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'.

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.

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.

Front

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

Back

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

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.

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.