Systems of Equations Word Problems

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The equations are represented as lines on a graph, and the solution is the point where the lines intersect.

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 elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you find the midpoint of a line segment?

Back

The midpoint is found by averaging the x-coordinates and the y-coordinates of the endpoints: ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the distance formula?

Back

The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is a word problem in the context of systems of equations?

Back

A real-world scenario that can be modeled using a system of equations to find unknown values.

Front

How can you represent a word problem as a system of equations?

Back

Identify the unknowns, create equations based on the relationships described in the problem, and express them in standard form.

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.