ACP Algebra 2 Chapter 3 (Systems) 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.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What does it mean for a solution to be a point of intersection?

Back

A point of intersection is where two lines (or curves) meet on a graph, representing the values of the variables that satisfy both equations.

Front

What is the graphical representation of a system of inequalities?

Back

The graphical representation shows shaded regions on a coordinate plane, indicating all possible solutions that satisfy the inequalities.

Front

Define 'objective function' in the context of linear programming.

Back

An objective function is a mathematical expression that defines the goal of optimization, typically to maximize or minimize a quantity.

Front

What is the feasible region in linear programming?

Back

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

Front

How do you determine the corner points of a feasible region?

Back

Corner points are found by identifying the vertices of the feasible region, which are the intersection points of the boundary lines.

Front

What is the significance of corner points in optimization problems?

Back

Corner points are significant because the maximum or minimum values of the objective function occur at these points in a linear programming problem.

Front

What is a linear inequality?

Back

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.