Alg. Ch. 5 Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How can you graphically represent a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where all equations are satisfied.

Front

What is a linear inequality?

Back

An inequality that involves a linear expression, representing a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality.