Solving Linear Equations

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. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean if a linear equation has no solution?

Back

A linear equation has no solution when the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

A linear equation has infinitely many solutions when the two equations represent the same line, meaning every point on the line is a solution.

Front

What is a unique solution in the context of linear equations?

Back

A unique solution occurs when the lines represented by the equations intersect at exactly one point.

Front

How do you solve the equation 8x + 4 = 4(2x + 1)?

Back

First, simplify the right side: 8x + 4 = 8x + 4. Since both sides are equal, the equation has infinitely many solutions.

Front

How do you solve the equation 3x - 7 = 3(x - 3) + 2?

Back

First, simplify the right side: 3x - 7 = 3x - 9 + 2. This simplifies to 3x - 7 = 3x - 7, which has infinitely many solutions.

Front

What is the solution to the equation -3(1 + 9x) - 7(-12x + 1) = 1 + 10x - 11 - 6x?

Back

The solution is x = 0.

Front

How do you solve the equation 3(x - 4) = 2(-2x + 1)?

Back

Distributing gives 3x - 12 = -4x + 2. Adding 4x to both sides results in 7x - 12 = 2, leading to x = 2.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation.