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 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 two sides of the equation 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 any value for the variable satisfies the equation. This usually happens when the two sides of the equation are equivalent, representing the same line.

Front

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

Back

No Solution

Front

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

Back

Infinite Solutions

Front

What is the solution to the equation: 0 = 0?

Back

Infinite Solution

Front

Solve the equation: 6(m + 3) = 2(m + 5)

Back

One Solution

Front

Solve the equation: -16 + 5n = -7(-6 + 8n) + 3

Back

One 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope 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.