Algebra Final Review Part 3 Systems, 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 to solve a system of equations by elimination?

Back

It involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in 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

How do you represent a system of inequalities graphically?

Back

By shading the region that satisfies all inequalities, with boundary lines indicating where the inequalities are equal.

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the point(s) where the equations intersect, indicating the values of the variables that satisfy all equations.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

How do you determine the number of solutions in a system of inequalities?

Back

By analyzing the shaded regions of the graph; if they overlap, there are solutions; if not, there are none.

Front

What is the first step in solving a word problem involving a system of equations?

Back

Identify the variables and write the equations based on the relationships described in the problem.

Front

What is the role of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.