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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel and never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

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 y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the significance of the point (0, b) in a linear equation?

Back

It is the y-intercept, where the line crosses the y-axis.

Front

What does the slope of a line represent?

Back

The rate of change of y with respect to x; it indicates the steepness of the line.