One Solution, No Solution, Infinite Solutions

Front

What are the three types of solutions for a system of equations?

Back

One solution, no solution, infinite solutions.

Front

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

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

How can you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

What is the condition for a system of equations to have exactly one solution?

Back

The lines represented by the equations must intersect at exactly one point.

Front

What does it mean to simplify an equation?

Back

To combine like terms and reduce the equation to its simplest form.

Front

In the equation 3x + 15 = 3(x + 5), what does it indicate if both sides are equal after simplification?

Back

It indicates that there are infinitely many solutions.

Front

What is the significance of the term 'missing information' in the context of equations?

Back

It refers to a variable or constant that, if altered, can change the number of solutions the equation has.

Front

What is the result of the equation 4x + 5 = 4x - 6?

Back

No solution, because simplifying leads to a contradiction (5 = -6).

Front

How do you identify if an equation has infinite solutions?

Back

If, after simplification, both sides of the equation are identical.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.