Algebra Final Review Part 3 Systems, Equations and Inequalities

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

It means 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

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

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 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 is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

How can you check if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into both equations to see if they hold true.