Systems of Equations

Front

What is a system of equations?

Back

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

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

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

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

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

Back

An inconsistent system has no solutions, meaning the equations do not intersect at any point.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

What is the substitution method for solving systems of equations?

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 for solving systems of equations?

Back

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

Front

How can you represent a real-world problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and set them equal to each other.

Front

What is the importance of finding the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, indicating the values of the variables that satisfy all equations.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations: parallel lines have no solutions, identical lines have infinite solutions, and intersecting lines have one solution.