2-4 Equations With No Solutions or Infinitely Many 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 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 make the equation true, meaning the two sides of the equation are never equal.

Front

Solve: 12 (x + 3) = 4 (2x + 9) + 4x

Back

Infinite Solutions

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Simplify: 5x + 6 = 2 + 3x. What type of solution does it have?

Back

One Solution

Front

What is the solution to the equation 3r - 5 = 2r?

Back

r = 5

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 is the significance of the coefficients in an equation?

Back

Coefficients determine the slope and position of the line represented by the equation.

Front

What is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.