Infinite/No 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 that can satisfy the equation, meaning the lines represented by the equations are parallel.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value that satisfies the equation, meaning the lines represented by the equations 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 satisfies the equation, meaning the lines represented by the equations are the same line.

Front

Solve for r: 3r - 5 = 2r - 7

Back

r = 5

Front

Solve for z: 8z - 22 = 9z - z + 33

Back

No Solution

Front

Solve for x: 5x + 9 = 4x + 9

Back

One Solution (x = any real number) because both sides simplify to 9.

Front

Solve for m: 6(m+3)=2m+10

Back

One Solution (m = 1) because both sides simplify to the same value.

Front

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

Back

No Solution (the equation simplifies to a false statement).

Front

What is the first step in solving linear equations?

Back

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

Front

What is the significance of parallel lines in the context of solutions to equations?

Back

Parallel lines indicate that the equations have no solution because they never intersect.