# Linear Equations in Two Variables Practice Set 1.3

Hi friends, welcome on Maths Master, here you will learn how to solve linear equations in two variables by using Determinant methods or Cramer’s Rule.

## Gabriel Cramer :

(31 July, 1704 to 4 January, 1752)
This Swiss mathematician was born in Geneva. He
was very well versed in mathematics, since childhood. At
the age of eighteen, he got a doctorate. He was a professor
in Geneva.

Using determinants, simultaneous equaions can be solved easily and in less space. This method is known as determinant method. This method was first given by a Swiss mathematician Gabriel Cramer, so it is also known as Cramer’s method.

To use Cramer’s method, the equations are written as a1x + b1y = c1 and a2x + b2y = c2.

To fine the value of x and y, first we have to find the value of D, Dx and Dy with the help of given below formula.

## Steps to solve linear equation in two variables by Cramer’s Rule:

• Write given equations in the form ax + by = c .
• Find the values of determinants D, Dx and Dy
• Using, x = Dx/D and y = Dy/D find values of x, y.

## Let’s see solved examples:

Solve the following simultaneous equations using Cramer’s Rule.
1. 5x + 3y = -11 ; 2x + 4y = -10

Sol.:

5x + 3y = -11 …………………………(1)

2x + 4y = -10 …………………………(2)

a1=5, b1=3, c1=-11

a2=2, b2=4, c2= -10

Now try to solve below examples, you can take hint from my video, link given below.