Systems of Linear Equations Application

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. Solutions are the points where the equations intersect.

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Front

How do you represent a system of equations graphically?

Back

By plotting each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

What is the role of coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation.

Front

What is the meaning of the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis, representing the value of y when x=0.