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.

Front

What is the elimination method?

Back

A technique for solving systems of equations by removing one variable, allowing for easier solving.

Front

What is the substitution method?

Back

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

Front

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

Back

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

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

Front

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

Back

If the lines intersect at exactly one point, the system has one unique solution.

Front

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

Back

The equations are represented as lines on a coordinate plane.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you say about the system?

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The system has infinitely many solutions because the second equation is a multiple of the first.