Solving Systems 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 point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Front

How do 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 and check if both equations are true.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect on a graph?

Back

The intersection point represents the solution to the system of equations.

Front

What does it mean if two lines are parallel?

Back

The system of equations has no solution because the lines never intersect.

Front

What does it mean if two lines coincide?

Back

The system of equations has infinitely many solutions because the lines are the same.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the slope of a line from its equation?

Back

Identify the coefficient of x in the slope-intercept form.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).