Solving Systems of Linear Equations by Graphing

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines intersect at exactly one point, which is the solution to the system.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you graph a linear equation in slope-intercept form?

Back

Identify the slope (m) and y-intercept (b) from the equation y = mx + b, then plot the y-intercept and use the slope to find another point.

Front

What is the slope of the line represented by the equation y = 3x + 6?

Back

The slope is 3.

Front

What is the y-intercept of the line represented by the equation y = 3x + 6?

Back

The y-intercept is 6.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect on the graph.

Front

What is the first step in solving a system of linear equations by graphing?

Back

Convert each equation to slope-intercept form (y = mx + b) if necessary.

Front

If two lines have the same slope but different y-intercepts, what can you conclude?

Back

The system has no solution because the lines are parallel.