One Solution, No Solution, Infinitely Many Solutions

What is a linear equation?

• An equation that makes a straight line when graphed.

• An equation that represents a curve on a graph.

• An equation that has no solutions.

• An equation that only contains constants.

How can you check if your solution is correct?

• Substitute the solution back into the original equation.

• Ignore the solution and move to the next problem.

• Ask a peer for their opinion on the solution.

• Rewrite the equation in a different form.

Solve the equation: 3(x-2) + 1 = 3x - 5

• One Solution

• No Solution

• Infinite Solutions

• Two Solutions

What is a dependent equation?

• An equation that has a unique solution.

• An equation that has infinite solutions because it represents the same line.

• An equation that has no solutions at all.

• An equation that is always true regardless of the variable.

What is a contradiction in equations?

• A situation where all values satisfy the equation, leading to infinite solutions.

• A situation where no values satisfy the equation, leading to no solution.

• A situation where at least one value satisfies the equation, leading to a unique solution.

• A situation where the equation is always true, regardless of the values.

Simplify and determine the solution: 3x - 7 = 3(x - 3) + 2

• No Solution

• One Solution

• Infinite Solutions

• Two Solutions

What does it mean if an equation has infinite solutions?

• It means that no matter what constant is substituted in for the variable, the equation is ALWAYS true.

• It means that the equation has no solutions at all.

• It means that the equation has exactly one solution.

• It means that the equation can have multiple solutions, but not infinite.

What is the general form of a linear equation?

• Ax + By = C, where A, B, and C are constants.

• y = mx + b, where m is the slope and b is the y-intercept.

• x^2 + y^2 = r^2, which represents a circle.

• y = a + bx, which is the equation of a linear regression.

What is the first step in solving an equation?

• Isolate the variable on one side of the equation.

• Combine like terms on both sides.

• Multiply both sides by the same number.

• Check the solution by substituting back.

What does it mean if an equation has no solution?

• It means that no matter what constant is substituted in for the variable, the equation will NEVER be true.

• It means that the equation can be solved for at least one value of the variable.

• It means that the equation has infinitely many solutions.

• It means that the equation is true for all values of the variable.