Solving Systems of Linear Equations

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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 graphical representation of a system of linear equations?

Back

The intersection points of the lines representing the equations.

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of linear equations?

Back

The system has infinite solutions because the lines are the same.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

Front

How do you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the lines intersect.

Front

What is a unique solution in a system of linear equations?

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A single point where the lines intersect, indicating one solution for the variables.

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on a graph.