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 linear equations?

Back

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

Front

What is substitution 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

What is elimination in 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 if a system has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

What is a unique solution in a system of equations?

Back

A single point where the lines intersect, representing one set of values for the variables.

Front

How do you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

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

Back

The equations are represented as lines on a coordinate plane, and their intersection points represent the solutions.

Front

What is the role of coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation.