Systems of equations and inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is an inconsistent system of equations?

Back

A system that has no solution because the equations represent parallel lines.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions because the equations represent the same line.

Front

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

It means that the coordinates of the point satisfy all equations in the system.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

By substituting the point's coordinates into each inequality and checking if all inequalities are satisfied.

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 that satisfy the inequality.