Question

. Solve for x and y:
bx + ay = a² + b² and x + y = 2ab.
ab​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x = \frac{a {}^{2} + b {}^{2} - 2a^{2}b}{b - a}}}}$

$\large{\underline{\boxed{\sf y = \frac{a {}^{2} + b {}^{2} - 2ab {}^{2} }{a - b}}}}$

Step-by-step explanation:

Given that ;

• bx + ay = a² + b² .... (i)
• x + y = 2ab ...... (ii)

We will solve this question using the elimination method. Here we go;

Step 1:

Multiplying equation (i) by 1 and equation (ii) by b.

• bx + ay = a² + b².....(iii)
• bx + by = 2ab²...... (iv)

Step 2:

Subtracting equation (iii) from (iv) -

(bx - bx) + (ay - by) = a² + b² +2ab²

⇒ y (a - b) = a² + b² + 2ab

⇒ y = $\sf \dfrac{a^2 + b^2 - 2ab^2}{a - b}$

Hence, the value of y is found.

_______________________

Again, consider the first and second equation ;

• bx + ay = a² + b² ..... (i)
• x + y = 2ab ..... (ii)

Again, we will apply elimination method ;

Step 1:

Multiplying equation (i) by 1 and equation (ii) by a.

• bx + ay = a² + b² .... (v)
• ax + ay = 2a²b..... (vi)

Step 2:

Subtracting (v) from (vi) -

(bx - ax) + (ay - ay) = a² + b² - 2a²b

⇒ x(b - a) = a² + b² - 2a²b

⇒ x = $\sf \dfrac{a^2 + b^2 - 2a^2 b}{b-a}$

Hence, the value of x is found.

_______________________

Therefore, the value of x and y are:

$\boxed{ \bf x = \frac{a {}^{2} + b {}^{2} - 2a^{2}b}{b - a} }$

$\boxed{ \bf y = \frac{a {}^{2} + b {}^{2} - 2ab {}^{2} }{a - b} }$