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 if two lines are parallel in a linear system?

Back

If two lines are parallel, it means they have the same slope and will never intersect, resulting in no solution for the system.

Front

What is the solution of a linear system with infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine the solution of a linear system graphically?

Back

The solution is found at the point where the lines intersect on the graph.

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?

Back

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

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, typically represented by parallel lines.

Front

How can you tell if a system of equations has one solution?

Back

A system has one solution if the lines intersect at exactly one point, meaning they have different slopes.

Front

What is the graphical representation of the equation x + 2y = -3?

Back

The graph is a straight line that can be plotted by finding the x and y intercepts.