3.3 Remediation Flashcard Linear Systems

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you solve a system of linear equations?

Back

You can solve a system of linear equations using substitution, elimination, or graphing methods.

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation of a system of inequalities shows a shaded region that represents all possible solutions.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation has an equal sign (=) while a linear inequality uses inequality signs (<, >, ≤, ≥) to show a range of solutions.

Front

How do you write a linear inequality from a word problem?

Back

Identify the variables, determine the constraints, and express the relationship using inequality symbols.

Front

What does the term 'feasible region' mean in linear programming?

Back

The feasible region is the area on a graph that satisfies all the constraints of a linear programming problem.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is written as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Front

How can 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.