One Solution, No Solution, or Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation. This often occurs when simplifying leads to a false statement, such as 0 = 5.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value for the variable that makes the equation true. This is the most common case in linear equations.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value for the variable satisfies the equation. This occurs when both sides of the equation are equivalent after simplification.

Front

Solve the equation: 3x - 8 = 3(x - 4) + 1

Back

No solutions.

Front

Solve the equation: -3(x + 6) = -3(2x + 4)

Back

One solution.

Front

Solve the equation: 14 - 2(3p + 1) = 6(4 + p)

Back

One solution.

Front

Solve the equation: 6x + 9 - x = 3x + 9 + x

Back

No solutions.

Front

Solve the equation: 3x + 15 = 3(x + 5)

Back

Infinitely many solutions.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one, and it can be written in the form ax + b = c.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation. They affect how steep the line is and where it intersects the axes.