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 linear equations?

Back

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

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

Front

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

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

How do you determine if a system of equations has one solution?

Back

The equations represent lines that intersect at exactly one point.

Front

What is the graphical representation of a system of linear equations?

Back

The lines of the equations plotted on a coordinate plane.

Front

How can you check your solution for a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.

Front

What is the role of coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line in a graph.