Final Exam Review: Applications of Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables. The solution to a linear system is the point(s) where the equations intersect.

Front

What does it mean to solve a linear system graphically?

Back

Solving a linear system graphically involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

What is the elimination method in solving linear systems?

Back

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

Front

Define 'dependent' and 'independent' systems of equations.

Back

Dependent systems have infinitely many solutions (the equations represent the same line), while independent systems have exactly one solution (the equations represent different lines that intersect at one point).

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions (the equations represent parallel lines that never intersect).

Front

How do you represent a real-world problem as a linear system?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations reflect the constraints given.

Front

What is the importance of the coefficients in a linear equation?

Back

Coefficients represent the rate of change or the weight of each variable in the equation, affecting the slope and position of the line when graphed.

Front

How can you check the solution of a linear system?

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.

Front

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

Back

The constant term represents the y-intercept of the line when graphed, indicating where the line crosses the y-axis.