Solving 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 do parallel lines indicate in a system of equations?

Back

They indicate that there is no solution, as they never intersect.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

How can you determine if a system has one solution?

Back

If the lines representing the equations intersect at exactly one point.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you find the intersection point of two lines graphically?

Back

By plotting both lines on the same graph and identifying the point where they cross.

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.