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 for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solutions?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means the lines are the same line, overlapping completely.

Front

How can you determine if a system of equations has one solution, no solutions, or infinite solutions?

Back

By graphing the equations and observing the intersection points.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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 is the graphical method for solving systems of equations?

Back

A method where each equation is graphed, and the solution is the intersection point.

Front

If the equations are 3x - y = 2 and 2x + y = 4, what is the solution?

Back

(2, 2) is the solution.

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.