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 for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have infinite solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

How do you graph a linear equation?

Back

Identify the y-intercept and slope, then plot the y-intercept and use the slope to find another point.

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 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 y-intercept of the equation y = 5x + 3?

Back

3, which is the point where the line crosses the y-axis.

Front

What is the slope of the equation y = -2x + 3?

Back

-2, indicating the line falls as it moves from left to right.

Front

How do you find the solution to a system of equations algebraically?

Back

By using substitution or elimination methods to solve for the variables.