Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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What does it mean for a system of linear equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What is the graphical representation of a system of linear equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect on a graph?

Back

The point of intersection represents the solution to the system of equations.

Front

What is the significance of the point (3, 0) in a system of linear equations?

Back

It is a solution where x=3 and y=0, satisfying both equations.

Front

What does it mean if two lines are parallel in a system of linear equations?

Back

The system has no solution because the lines never intersect.

Front

What is the meaning of 'no solution' in a system of linear equations?

Back

It indicates that the equations represent parallel lines that do not intersect.

Front

What is the meaning of 'infinitely many solutions' in a system of linear equations?

Back

It occurs when the equations represent the same line, leading to an infinite number of intersection points.

Front

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

Back

By finding the point where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of linear equations?

Back

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