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 does it mean if two lines are parallel when graphing a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: if slopes are equal and intercepts are different, no solution; if slopes are equal and intercepts are the same, infinitely many solutions; if slopes are different, one 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 do you find the y-intercept of a line?

Back

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

Front

What is the significance of the point (1, 3) in a system of equations?

Back

It is a solution to the system, meaning both equations are satisfied at this point.

Front

What does the term 'no solution' indicate in a system of equations?

Back

It indicates that the equations represent parallel lines that do not intersect.