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 = 0, where a and b are constants.

Front

What does it mean for a linear equation to have infinite solutions?

Back

A linear equation has infinite solutions when it represents the same line in a graph, meaning any value of x will satisfy the equation. For example, 4x + 10 = 4x + 10.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Front

What is the solution to the equation 7x - 3x - 8 = 24?

Back

The solution is x = 8.

Front

What is the solution to the equation -4x = 24?

Back

The solution is x = -6.

Front

How do you distribute in an equation?

Back

To distribute, multiply each term inside the parentheses by the term outside. For example, in 2(2x + 3), you would calculate 2*2x and 2*3.

Front

What is the solution to the equation 2(2x + 3) = -6(x + 9)?

Back

The solution is x = -6.

Front

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

Back

The coefficient is the number that multiplies the variable. It determines the slope of the line when graphed.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in infinitely many solutions.