Systems STAAR Review

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 one solution?

Back

It means the lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

It means the lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

It means the equations represent the same line, so there are countless points that satisfy both equations.

Front

How do you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the general form of a linear equation?

Back

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 is a measure of the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

How can you represent a real-world problem as a system of equations?

Back

By defining variables for the unknowns and creating equations based on the relationships described in the problem.

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.