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 if two lines intersect on a graph?

Back

It means that the system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

It means that the system of equations has no solution.

Front

What does it mean if two lines are the same on a graph?

Back

It means that the system of equations has infinite solutions.

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 solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

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

What does the term 'feasible region' refer to in linear programming?

Back

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

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3,0) is the solution.