Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean to solve a linear system?

Back

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

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What is the point of intersection in a linear system?

Back

The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

Front

What are the possible outcomes when solving a linear system?

Back

1. One solution (intersecting lines), 2. No solution (parallel lines), 3. Infinitely many solutions (coincident lines).

Front

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

Back

A system has no solution if the equations represent parallel lines, which never intersect.

Front

What is the substitution method in solving linear systems?

Back

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

Front

What is the elimination method in solving linear systems?

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

Front

What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines.