How Many Solutions Multi-Step Equations

Front

What is a system of equations?

Back

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

Front

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

Back

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

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has one solution?

Back

It means that the equations intersect at exactly one point, which is the solution.

Front

How can you determine if two equations are equivalent?

Back

If you can manipulate one equation to become the other through algebraic operations, they are equivalent.

Front

What is the first step in solving a multi-step equation?

Back

Identify and isolate the variable by performing inverse operations.

Front

What is the significance of simplifying equations?

Back

Simplifying equations helps to make them easier to solve and understand.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

How do you solve for a variable in an equation?

Back

You isolate the variable on one side of the equation using inverse operations.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed and has no variables raised to a power greater than one.