Equations

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equal sign (=). The goal in solving an equation is to find the value of the variable that makes the equation true.

Linear Equations

A linear equation is an equation in which the highest power of the variable is 1. Its general form is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

Quadratic Equations

A quadratic equation is an equation in which the highest power of the variable is 2. Its general form is ax² + bx + c = 0, where a, b, and c are constants. Quadratic equations can be solved using methods such as factoring, completing the square, or using the quadratic formula.

Solving Equations

To solve an equation, you perform operations on both sides of the equation to isolate the variable. The goal is to get the variable on one side of the equation and the constants on the other side. The operations include addition, subtraction, multiplication, division, and taking square roots.

Systems of Equations

A system of equations is a set of two or more equations with the same variables. The solution to a system of equations is the values of the variables that satisfy all the equations simultaneously.

Understanding equations and how to solve them is fundamental in mathematics and has many real-world applications in fields such as physics, engineering, economics, and more.