Mini Flashcard 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 the graphical representation of a system of linear equations?

Back

The intersection points of the lines representing the equations.

Front

What is the substitution method 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 the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

Front

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

Back

The system has infinitely many solutions because the lines are the same.

Front

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

Back

Align the equations so that like terms are in the same column.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.