**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.**

**Click here for Practice Set 1.1 Elimination Method**

## 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 a_{1}x + b_{1}y = c_{1} and a_{2}x + b_{2}y = c_{2}.

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.

**Click here for Practice Set 1.2 Graphical Method**

## 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)

a_{1}=5, b_{1}=3, c_{1}=-11

a_{2}=2, b_{2}=4, c_{2}= -10

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

## Practice Set : 1.3

Click Here For Video Solution

## More Questions for Your Practice

- 3x – y = 7 ; x + 4y = 11
- 4x +3y =4 ; 6x +5y = 8
- 3x – 4y = 7 ; 5x + 2y = 3
- 3x – 4y = 10; 4x + 3y = 5
- 4m – 2n = – 4; 4m + 3n =16

Ans.: 1. (3,2), 2. (-2,4) , 3. (1,-1)

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