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 the variable 'x' typically represent in a system of equations?

Back

In word problems, 'x' often represents the quantity of one type of item or group being analyzed.

Front

What does the variable 'y' typically represent in a system of equations?

Back

In word problems, 'y' often represents the quantity of another type of item or group being analyzed.

Front

How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane. The point where the lines intersect represents the solution to the system.

Front

What is the substitution method for 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 for 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

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.