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 on a graph.

Front

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

Back

A system of equations has no solution when the graphs of the equations are parallel lines, meaning they never intersect.

Front

What is the graphical representation of intersecting lines?

Back

Intersecting lines represent a system of equations with one unique solution, where the lines cross at a single point.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line. A positive slope means the line rises, while a negative slope means it falls.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How can you represent a system of inequalities graphically?

Back

A system of inequalities can be represented by shading the regions of the graph that satisfy the inequalities, with boundary lines indicating where the inequalities change.

Front

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

Back

A linear equation shows a relationship that is equal, while a linear inequality shows a relationship that is greater than or less than.

Front

What does the term 'feasible region' mean in the context of inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system are satisfied, representing all possible solutions.

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.