Systems and Word Problems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

How do you solve a system of equations by 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 does it mean to solve for x and y in a system of equations?

Back

Finding the values of x and y that satisfy all equations in the system simultaneously.

Front

What is the graphical interpretation of a system of equations?

Back

The solutions are the points where the graphs of the equations intersect.

Front

Define 'linear equation'.

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is the purpose of using variables in word problems?

Back

Variables represent unknown quantities that we need to find.

Front

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

Back

Identify the unknowns, create equations based on the relationships described in the problem.

Front

What is the elimination method for solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

If a system of equations has no solution, what does that mean?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.