System Of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

It means the lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

How do you solve a system of equations by graphing?

Back

1. Graph both equations on the same coordinate plane. 2. Identify the point(s) where the lines intersect.

Front

What is the slope of a line in the context of a system of equations?

Back

The slope indicates the steepness of the line and is calculated as the change in y over the change in x.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

If two equations have the same slope but different y-intercepts, what can be said about their solutions?

Back

The system has no solution because the lines are parallel.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines intersecting at a single point.