Linear Equations: Number of Solutions

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 does it mean if a linear equation has one solution?

Back

It means that there is exactly one value for the variable that makes the equation true.

Front

What does it mean if a linear equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean if a linear equation has infinite solutions?

Back

It means that any value for the variable will satisfy the equation, indicating that the two sides of the equation are equivalent.

Front

Solve for g: 2(3g + 1) = 3g + 1 + 3g

Back

No Solution.

Front

Solve for e: 6e ‒ 10 = 10 ‒ 2e + 10e

Back

One Solution.

Front

Solve for p: –8 ‒ 4p = 5(p + 2)

Back

One Solution.

Front

Solve for q: –2q ‒ 3 = –2q ‒ 8

Back

No Solution.

Front

Solve for b: 2b ‒ 5 = 9

Back

One Solution.

Front

What is the graphical representation of a linear equation with one solution?

Back

A single point where the two lines intersect.