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

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

Front

What is graphing in the context of systems of equations?

Back

Graphing involves plotting the equations on a coordinate plane to visually find the point(s) of intersection, which represent the solution.

Front

What is the difference between a variable and a constant?

Back

A variable is a symbol that represents an unknown value, while a constant is a fixed value that does not change.

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

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Front

If the sum of two numbers is 13 and their difference is 3, what are the numbers?

Back

The numbers are 8 and 5.

Front

In the context of systems of equations, what does 'consistent' mean?

Back

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