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 graphical representation of a system of linear equations?

Back

The intersection point(s) 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 infinitely many 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

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

Back

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

Front

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

Back

If the lines are parallel, they do not intersect, indicating no solution.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0) - This is the point where the two lines intersect.