One, None 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 does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation. This typically occurs when the equations represent lines that intersect at a single point.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when there are countless values for the variable that satisfy the equation. This usually happens when the equations represent the same line.

Front

Solve for x: 5x + 4 = 3(2x - 5) - (x + 5)

Back

No Solution

Front

Solve for w: -7w + 4 = -3(w + 3) - 2(w + 1)

Back

One Solution

Front

Solve for e: 3(3e + 7) - 7(e + 3) = 5(e - 2) - 2(e + 1)

Back

One Solution

Front

Solve for x: 6x - 18 = 4(2x - 3) - (2x + 6)

Back

Infinite Solution

Front

Solve for x: -5(2x - 4) = 2(10 - 5x)

Back

Infinite Solution

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What is the graphical representation of no solution?

Back

The graphical representation of no solution is two parallel lines that never intersect.