No Solution/Infinite Solution/One Solution

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 two sides of the equation represent parallel lines that never intersect.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation. This typically happens when the two sides of the equation are equivalent expressions.

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 makes the equation true. This is represented by the intersection of two lines at a single point.

Front

Solve for x: 8z - 22 = 3(3z + 11) - z

Back

No Solution

Front

Solve for x: x + 6 = x

Back

No Solution

Front

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

Back

Infinite Solutions

Front

Solve for x: 4x - 9 = 3.5x - 9

Back

x = 0

Front

Solve for x: 8x + 4(4x − 3) = 4(6x + 4) − 4

Back

No 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 significance of the slope in a linear equation?

Back

The slope of a linear equation indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.