Systems of Equations - Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

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 the equations reflect the problem's constraints.

Front

What does it mean when two equations are consistent?

Back

Two equations are consistent if they have at least one solution in common.

Front

What does it mean when two equations are independent?

Back

Two equations are independent if they have exactly one solution, meaning the lines intersect at a single point.

Front

What does it mean when two equations are dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

Substitute the values of the variables back into the original equations to see if they satisfy all equations.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the meaning of 'perimeter' in a word problem?

Back

Perimeter refers to the total distance around a two-dimensional shape, calculated by adding the lengths of all sides.