Flashcard 6M: System of linear equations

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 if a system of linear equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at a single point.

Front

How do you find the solution to a system of linear equations graphically?

Back

Plot both equations on a graph and identify the point where they intersect.

Front

What is the constant of variation in a direct variation equation?

Back

It is the ratio of y to x, represented as k in the equation y = kx.

Front

If y varies directly with x and y = 7 when x = 14, what is the constant of variation?

Back

1/2

Front

What does it mean if two lines are the same line in a system of equations?

Back

The system has infinitely many solutions.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

If the equations are equivalent, they represent the same line.

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.