Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over 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

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If the equations are satisfied, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of each equation plotted on the same coordinate plane.

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

The intersection point represents the solution to the system of equations, where both equations are satisfied.