Question

3. If ax+by = a^2-b^2 and bx + ay = 0. find the
value of x + y.​

Answer 1

Answer:

The value of (x + y) is (a - b)

Step-by-step explanation:

ax+by = a^2-b^2

Multiply both sides by b.

abx+(b^2)y= b(a^2-b^2) ------ [1]

bx + ay = 0

Multiply both sides by a.

abx+(a^2)y=0 ------[2]

By doing Equation [1] - Equation [2] we get,

(b^2)y - (a^2)y = b(a^2-b^2)

or, y= -b ------- [3]

bx + ay = 0

Put y= -b  (We get it from equation [3])

So, bx + a(-b)=0

or, x= a ------[4]

So, by doing [3] + [4] we get

x+y = a-b

Answer 2

Answer:

The value of x+y = a-b

Step-by-step explanation:

$ax + by = {a}^{2} - {b}^{2} ......(1) \\ bx - ay = 0.....(2) \\ add \: equations \: (1) \: and \: (2) \\ ax + bx + by + ay = {a}^{2} - {b}^{2} \\ taking \: x \: as \: common \: from \: first \: 2 \: terms \: and \: y \: as \: common \: from \: last \: 2 \: terms \: we \: get \\ x(a + b) + y(a + b) = {a}^{2} - {b}^{2} \\ again \: taking \: (a + b) \: as \: common \: we \: get \\ (a + b)(x + y) = {a}^{2} - {b}^{2} \\ we \: know \: that \: {a}^{2} - {b}^{2} = (a + b)(a - b) \\ (x + y)( a+b ) = (a + b)(a -b ) \\ x + y = \frac{( a+b )(a -b )}{(a + b)} \\ x + y = a - b$