Q) Solve for x and y : √2 x + √3 y = 5 and √3 x – √8 y = -√6

PYQ: Q 21 (b) – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans: 

To solve for x and y, we need to solve the given system of equations:

√2 x + √3 y = 5 …………….. (i)

and √3 x – √8 y = – √6  ………………. (ii)

Step 1: Let’s start by simplifying the equation (ii), we can write it as:

√3 x – 2 √2 y = – √6 …………………… (ii)

Step 2: Since we need to solve this set of equations for values of x and y, let’s solve for y first.

To do this, we need to equal the coefficients of x and then subtract one equation form other to cancel out x:

∴ First, we multiply equation (i) by √3 and multiply equation (ii) by √2, we get:

∴ √3 (√2 x + √3y) = 5 (√3)

∴ √6 x + 3 y = 5 √3 ………………. (iii)

Similarly, √2 (√3 x – 2 √2 y) = (- √6) (√2)

∴ √6 x – 4 y = – 2 √3 …………………. (iv)

Step 3: Next, let’s subtract equation (iv) from equation (iii):

(√6 x + 3 y) – (√6 x – 4 y) = 5√3 – (- 2√3)

∴ √6 x + 3 y – √6 x + 4 y = 5√3 + 2√3

∴ 7 y = 7 √3

∴ y = √3

Step 4: Next, we substitute the value of y into equation (i) to find the value of x:

√2 x + √3 y = 5 …………….. (i)

∴ √2 x + √3 (√3) = 5

∴ √2 x + 3 = 5

∴ √2 x = 5 – 3

∴ √2 x = 2

∴ x = 2 /√2

∴ x = √2

Therefore, the value of x and y are x = √2 and y = √3.

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