Solving Equations with No Solution and Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when the equations represent parallel lines that never intersect.

Front

What is an example of an equation with no solution?

Back

An example is 2x + 3 = 2x - 5. Simplifying leads to 3 = -5, which is a contradiction.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation. This occurs when the equations represent the same line.

Front

What is an example of an equation with infinite solutions?

Back

An example is 3(x - 2) = 3x - 6. Simplifying leads to 0 = 0, which is always true.

Front

How do you determine if an equation has one solution, no solution, or infinite solutions?

Back

You can determine this by simplifying the equation. If you end up with a true statement (like 0=0), it has infinite solutions. If you get a false statement (like 3=-5), it has no solution. If you find a specific value for the variable, it has one solution.

Front

Solve: 5x - 14 = 8x + 4

Back

x = -6 (one solution).

Front

Solve: 3(x - 8) = 3x - 24

Back

Infinite Solutions.

Front

Solve: 12(y + 2) = 6(2y + 4)

Back

Infinite Solutions.

Front

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

Back

Infinitely Many Solutions.

Front

What is the significance of parallel lines in relation to solutions of equations?

Back

Parallel lines indicate that the equations have no solution because they never intersect.