Systems of Equations and Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that there are countless pairs of values that satisfy all equations in the system, often represented by the same line.

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

Front

What does it mean for a system of inequalities to be represented graphically?

Back

The solution set is shown as a shaded region on the graph, indicating all possible solutions.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point, while a solution to an inequality is a range of values.

Front

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

Back

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

Front

How do you find the slope of a line given two points?

Back

Use the formula m = (y2 - y1) / (x2 - x1).

Front

What does the term 'feasible region' refer to in systems of inequalities?

Back

The area on a graph where all constraints of the inequalities are satisfied.