Graphing Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a point to be a solution to a system of equations?

Back

The point satisfies all equations in the system.

Front

How can you determine if two lines represented by equations are parallel?

Back

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

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the intersection point.

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

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

Back

It is the point where the line crosses the y-axis.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute it into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract equations to eliminate one variable, then solve for the other.