Systems of Equations

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, having the same slope but different y-intercepts.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

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

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 can you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by multiplying or dividing by a non-zero number.

Front

What is the slope of a line in the context of a linear equation?

Back

The slope indicates the steepness of the line and is calculated as the change in y over the change in x (rise/run).

Front

What is a y-intercept?

Back

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

Front

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.