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 are parallel lines in the context of systems of equations?

Back

Lines that never intersect because they have the same slope.

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 of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

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 y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, y).

Front

How do you write the equation of a line in slope-intercept form?

Back

The equation is written as y = mx + b, where m is the slope and b is the y-intercept.