Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

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 graphical interpretation of a system of linear equations?

Back

The solutions to the system are the points where the lines intersect.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.

Front

How can you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the first step in solving word problems involving systems of equations?

Back

Identify the variables and what they represent in the context of the problem.

Front

What is the purpose of defining a system of equations in a word problem?

Back

To model the relationships between different quantities in the problem.

Front

How do you interpret the solution of a system of equations in a real-world context?

Back

The solution represents the values of the variables that satisfy all equations in the system.

Front

What is the role of the constant term in a linear equation?

Back

It represents the y-intercept of the line when the equation is in slope-intercept form.