Systems of Equations (All three methods)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The lines represented by the equations are the same line.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you write an equation for a linear relationship?

Back

Use the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope (m) is the ratio of the rise (change in y) over the run (change in x) between two points on the line.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the solution is the point(s) of intersection.

Front

What does it mean if two lines intersect at a single point?

Back

The system of equations has one unique solution.