Systems Word Problems

Front

What is a system of linear equations?

Back

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

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure they reflect the problem's constraints.

Front

What does it mean if two equations in a system are dependent?

Back

It means they represent the same line and have infinitely many solutions.

Front

What does it mean if two equations in a system are independent?

Back

It means they represent different lines and have exactly one solution.

Front

What does it mean if two equations in a system are inconsistent?

Back

It means they represent parallel lines and have no solutions.

Front

How can you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both equations to see if they hold true.

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 interpret the solution of a system of equations in a real-world context?

Back

The solution represents the values of the variables that satisfy all conditions of the problem.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the relationship between the variables in the equations, indicating how changes in one variable affect the other.