Flashcardizz #2 M8 Number of Solutions

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, meaning the two sides of the equation are equivalent for all values.

Front

What is a unique solution in an equation?

Back

A unique solution occurs when there is exactly one value of the variable that satisfies the equation.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation, meaning the two sides are never equal.

Front

Solve: 6x + 9 – x = 3x + 9 + x

Back

One Solution: x = 0.

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution.

Front

What is the first step in solving linear equations?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

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

Solve: 3x - 7 = 3(x - 3) + 2

Back

Infinite Solutions.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

What does it mean to isolate a variable?

Back

To isolate a variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.