Systems 12/12/24

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution.

Front

How do you represent a situation with a system of equations?

Back

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

Front

What is the first step in solving the equation 2x + 4y = 14 for y?

Back

Subtract 2x from both sides to isolate the term with y.

Front

What is the graphical representation of parallel lines in a system of equations?

Back

Parallel lines indicate that the system has no solutions, as the lines never intersect.

Front

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

Back

By analyzing the slopes and intercepts of the lines: intersecting lines have one solution, parallel lines have none, and coinciding lines have infinitely many.

Front

What is the purpose of using variables in a system of equations?

Back

Variables represent unknown quantities that we aim to solve for in the equations.

Front

What does the equation 5q + 2z = 1.32 represent in a real-world context?

Back

It represents a relationship between the cost of squash (q) and zucchini (z) based on given prices.

Front

How do you write a system of equations from a word problem?

Back

Extract key information, define variables, and translate the relationships into equations.

Front

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

Back

Coefficients indicate the rate of change or contribution of each variable in the equations.