Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2

#### Solution

The given equations are

√3x – √2y = √3 ….(1)

√5x – √3y = √2 ….(2)

Let us eliminate y. To make the coefficients of equal, we multiply the equation (1) by √3 and equation (2) by √2 to get

3x – √6y = 3 ….(3)

√10x + √6y = 2 ….(4)

Adding equation (3) and equation (4), we get

3x + √10x = 5 ⇒ (3 + √10) x = 5

`\Rightarrow \text{x}=\frac{5}{3+\sqrt{10}}=( \frac{5}{\sqrt{10}+3})\times( \frac{\sqrt{10}-3}{\sqrt{10}-3})`

`=5( \sqrt{10}-3)`

Putting x = 5( √10– 3) in (1) we get

√3 × 5(√10 – 3) –√2 y = √3

⇒ 5√30 – 15√3 – √2y = √3

⇒ √2y = 5√30 – 15√3 – √3

⇒ √2y = 5√30 – 16√3

`⇒ y=\frac{5\sqrt{30}}{\sqrt{2}}-\frac{16\sqrt{3}}{\sqrt{2}}`

⇒ y = 5√15 – 8√6

Hence, the solution is x = 5( √10– 3) and y = 5√15 – 8√6