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

The lines intersect at exactly one point on a graph.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

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 y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b).

Front

What is the slope of a linear equation?

Back

The rate of change of the line, calculated as rise over run (m = (y2 - y1) / (x2 - x1)).

Front

How do you determine the solution of a system graphically?

Back

By finding the point of intersection of the lines on a graph.