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 to solve a system of equations by graphing?

Back

It means to graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the solution to a system of equations?

Back

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

Front

What does it indicate if two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it indicate if two lines are parallel?

Back

The system has no solution.

Front

What does it indicate if two lines overlap completely?

Back

The system has infinitely many solutions.

Front

How do you find the y-intercept of a linear equation?

Back

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

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

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.