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.

Front

What does it mean for two lines to intersect on a graph?

Back

It means they have one solution, which is the point where they cross.

Front

What is the solution of a system of equations represented graphically?

Back

The point(s) where the lines intersect.

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are the same?

Back

They have infinite solutions because every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations; if both are true, it's a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

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 graphical method for solving systems of equations?

Back

Plotting both equations on a graph and identifying the intersection point.

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on a graph.