One Solution, No Solution, Infinite 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 + by = c, where a, b, and c are constants.

Front

What does it mean for a system of equations to have one solution?

Back

A system of equations has one solution when the lines intersect at exactly one point, meaning there is one unique solution for the variables.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines are parallel and never intersect, indicating that there is no set of values for the variables that satisfies both equations.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning any point on the line is a solution.

Front

Solve: 3x + 15 = 3(x + 5) - x

Back

x = 0

Front

Identify the second equation that makes the system have no solution: 3x + y = -5.

Back

3x + y = 4

Front

Simplify and determine the solution type: 3x - 8 = 3(x - 4) + 1

Back

No solutions

Front

Solve: 12(x + 3) = 4(2x + 9) + 5x

Back

x = 0

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

What is the graphical representation of a system with no solution?

Back

The graphical representation is two parallel lines that never intersect.