This blog notes down all key concepts and properties to remember to be able to solve problems related to GMAT linear and quadratic equations. Many GMAT Data Sufficiency & GMAT Problem Solving questions need basic know-how and knowledge of properties so we can infer if sufficient information is available or not.

This section needs to be revised at least once. **Before we delve into quadratic equations, we will take a look at the basic linear equations. **

**Linear Equations**

The **most basic equation is of the form y = mx + c**. Herein, m is the slope and c is the intercept for the equation. We have two variables here to be able to solve for the x and y. We will need at least two equations to solve for two variables.

Though in GMAT, you could solve for **y = mx + c** if there is additional information available such as the values of x and y being positive integers. This will eliminate any chance of them being 0 as well. Thus, t**his constraint can help us to be able to get the values of x and y. **

**Quadratic Equations**

The quadratic equations are equations with degree 2. So, the highest power of the variables is 2. They typically take the form of ax^2 + bx + c = 0. **Where a, b, c are constants. **

**Roots:**The roots for the equations is defined as**[-b +/- sqrt(b^2-4ac)]/2**a. The image above shows a neat representation of the same.**Sum/Product:**The sum of the roots is**(-b/a)**and the product of the roots is equivalent to**(c/a)**. Given b and c. We should be able to solve for both the roots. Two equations and two variables.

**Plug in Numbers**

The key to solving questions with variables within the problem statement is to use numbers to plugin for the variables and use POE aka process of elimination for the equations.

- e.g. Let’s say the problem statement ends up as a probable solution with values of 4K + 4 or 4K – 4.
- We can check for the right answer by pluggin in the value for K and seeing which answers don’t match the actual output.
**The right answers is among the non eliminated options.**By plugging in another number, we can further reduce the choices until we end up with one choice.- This is faster than trying to solve algebraically.