No Solution, One Solution, 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 simplifying leads to a false statement, such as 0 = 5.

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 the most common case in linear equations.

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 occurs when the equation simplifies to a true statement, such as 0 = 0.

Front

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

Back

m = -3. This equation has One Solution.

Front

Solve the equation: 8m+12=2(4m+6)

Back

This equation simplifies to a true statement (0=0), indicating Infinite Solutions.

Front

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

Back

m = -1. This equation has One Solution.

Front

Solve the equation: 12(y+2)=6(2y+4)

Back

This equation simplifies to a true statement (0=0), indicating Infinite Solutions.

Front

Solve the equation: 2(m+3)=2m+12

Back

This equation simplifies to a false statement (0=6), indicating No Solution.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one and can be graphed as a straight line.

Front

What is the significance of the variable in an equation?

Back

The variable represents an unknown value that we are trying to solve for in the equation.