Introduction to Linear Equations and the Cross Multiplication Method
Linear equations are equations of the first degree, meaning they involve only and raised to the power of one. These equations can graphically represent straight lines. When we deal with two linear equations simultaneously, finding a common solution means identifying the point where the lines intersect. To achieve this, we can use several methods, including the cross multiplication method.
The cross multiplication method is a systematic way to find the solution of two linear equations in two variables. This method is particularly useful when the equations are given in standard form:
In this article, we will delve deeply into the cross multiplication method, offering stepbystep explanations, practical examples, and relevant applications to help K12 students understand and apply this technique effectively.
Steps to Solve Using the Cross Multiplication Method
To use the cross multiplication method, follow these simple steps:

 Write the equations in standard form as shown above.
 Form the following determinant equations by cross multiplying the coefficients:
 Equate each of these fractions to find the values of and .
Let’s clarify these steps with a simple example:
Consider the pair of linear equations:
Putting these equations in the form:
Substituting these values into our determinant equation formula:
Therefore, and . Hence, the solution to the pair of linear equations is and .
RealWorld Applications
The cross multiplication method isn’t just for abstract mathematical exercises; it has practical realworld applications too. Here are a couple of examples:
 Financial Planning: Suppose you are entitled to receive is a share of profits from two different investment plans, both tied to stock prices which can be modeled as linear equations. Finding the equilibrium point can help you decide the optimal mix of investments.
 Physics: In physics, many problems involving motion, forces, and other parameters can be simplified to linear equations. From calculating precise points where two paths intersect to analyzing forces acting at a point, linear equations, and their solutions, hold vital significance.
Practice Problems
Practicing is crucial to mastering any mathematical concept. Here are some problems for you to solve using the cross multiplication method:
Solve the following pair of equations:
Solve the following pair of equations:
Practice similar problems and crosscheck your solutions to grasp the concept firmly.
Conclusion
The cross multiplication method is a powerful and straightforward technique to solve pairs of linear equations. By ensuring a systematic approach and practicing regularly, K12 students can master this method and apply it in various mathematical and realworld scenarios.
Whether dealing with finance, physics, or just everyday problems, understanding and applying the cross multiplication method can offer elegant and efficient solutions.
Be sure to revisit the steps, practice the provided problems, and explore additional resources to reinforce your learning.