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 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 in a system of equations?

Back

They have the same slope and will never intersect, meaning there is no solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, having infinitely many solutions.

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: one solution (intersecting), no solution (parallel), or infinitely many solutions (coincident).

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 slope of a line given two points?

Back

Use the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

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

Back

The lines are parallel and do not intersect.