Systems of Equations Graphing Identify Solutions

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 plot the equations on a graph and identify the point(s) where they 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 a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you identify the solution from a graph?

Back

Look for the coordinates of the intersection point of the lines.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of a line?

Back

The rate at which y changes for a unit change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a line?

Back

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

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.