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 if a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

What is the elimination method for solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical representation of a system of equations?

Back

The graph shows the lines of the equations, and their intersections represent the solutions.

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3,0)

Front

Solve by substitution: y = 2x + 3 and 3x - y = 5.

Back

(1,5)