Solving Equations with No Solution and Infinite Solutions

Front

What is an equation with no solution?

Back

An equation with no solution is one that has no values for the variable that will satisfy it. For example, the equation 2x + 3 = 2x + 5 has no solution because there is no value of x that can make both sides equal.

Front

What is an equation with infinite solutions?

Back

An equation with infinite solutions is one where any value for the variable will satisfy the equation. For example, the equation 2(x + 1) = 2x + 2 has infinite solutions because both sides are equivalent for any value of x.

Front

Solve: 14 - 2(3p + 1) = 6(4 + p)

Back

p = -1

Front

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

Back

m = -2

Front

What does it mean if an equation simplifies to a false statement?

Back

If an equation simplifies to a false statement (like 0 = 5), it indicates that there is no solution.

Front

Solve: 3y + 6 + 4y - 7 = -8

Back

y = -1

Front

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

Back

Infinite Solutions

Front

What is the first step in solving an equation?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

Front

What is the significance of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.

Front

What does it mean if two equations represent the same line?

Back

If two equations represent the same line, they have infinite solutions because every point on the line is a solution to both equations.