5-2: Solve 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 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 will 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 intersection point of two lines graphically?

Back

By plotting both lines on a graph and locating the point where they cross.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

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