Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the equations intersect on a graph.

Front

How can you graph a system of linear equations?

Back

To graph a system of linear equations, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect. This intersection represents the solution to the system.

Front

What does the solution (x, y) represent in a system of linear equations?

Back

The solution (x, y) represents the coordinates of the point where the two lines intersect, indicating the values of the variables that satisfy all equations in the system.

Front

What is the significance of the intersection point in a graphed system of linear equations?

Back

The intersection point signifies the unique solution to the system, where all equations are satisfied simultaneously.

Front

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

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

Front

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

Back

If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

Front

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

Back

To determine the solution algebraically, you can use methods such as substitution, elimination, or matrix operations to find the values of the variables that satisfy all equations.

Front

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

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

Front

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

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing you to solve for the remaining variable.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.