Writing and Solving 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

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find 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 graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What does the solution (45,90) represent in the context of time taken for haircuts and hair dyes?

Back

Haircuts take Alexandra 45 minutes & hair dyes take 90 minutes.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

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

Back

Infinitely many solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

Identify the variables, write equations based on the relationships between them, and ensure they reflect the situation accurately.

Front

What is the importance of coefficients in a system of equations?

Back

Coefficients represent the rate of change or the quantity of each variable in the equations, affecting the solution.

Front

What does it mean if two equations in a system are dependent?

Back

Dependent equations are those that represent the same line, leading to infinitely many solutions.

Front

How do you find the cost of items using a system of equations?

Back

Set up equations based on the total cost and quantities of items, then solve the system to find the cost of each item.