System of Equations by Inspection

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

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

Back

A system has no solution when the equations represent parallel lines, which never intersect.

Front

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

Back

A system has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

Front

How can you find the solution to a system of equations graphically?

Back

You can find the solution by graphing the equations and identifying the point(s) where the lines intersect.

Front

What is the initial value (y-intercept) in a linear equation?

Back

The initial value, or y-intercept, is the value of y when x is 0, represented as (0, b) in the equation y = mx + b.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

The graphical representation shows two lines intersecting at a single point.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation shows two parallel lines that never intersect.