Solving 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 to the system is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting each equation on the same coordinate plane and identifying the point(s) where the graphs intersect.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the set of values for the variables that satisfy all equations in the system simultaneously.

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the graphs of the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

How can you determine the number of solutions in a system of equations?

Back

You can determine the number of solutions by analyzing the graphs of the equations: one intersection point indicates one solution, no intersection points indicate no solution, and overlapping lines indicate infinitely many solutions.

Front

What is the significance of the point (4, 0) in a system of equations?

Back

The point (4, 0) is a solution to the system of equations, meaning it is the point where the graphs of the equations intersect.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a straight line through those points.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the meaning of the slope in a linear equation?

Back

The slope of a linear equation represents the rate of change of y with respect to x; it indicates how steep the line is.