Solve Systems by Graphing

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 one solution?

Back

A system has one solution 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 graphs of the equations are parallel and 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 intersect at every point on that line.

Front

How can you determine the solution to a system of equations by graphing?

Back

To determine the solution by graphing, plot the equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

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

Back

The intersection point represents the values of the variables that satisfy all equations in the system.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.