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 point(s) where the equations intersect.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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 variable.

Front

What does it mean for a system of equations to be consistent?

Back

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

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the graphs of the equations are parallel and 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.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and set up the system based on the problem's context.

Front

What is the first step in solving a word problem involving a system of equations?

Back

Read the problem carefully to identify the variables and the relationships between them.

Front

In the horse and chicken problem, how do you set up the equations?

Back

Let h = number of horses and c = number of chickens. The equations are: h + c = 28 (total animals) and 4h + 2c = 80 (total legs).

Front

What is the importance of checking your solution in a system of equations?

Back

Checking your solution ensures that it satisfies all equations in the system, confirming its validity.