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solve the following equation
ax+by=b-a
bx-ay=-(a+b)​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\blue{\boxed{x = - 1,\:y = 1}}$

★ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ★

System of equations given are

$\to ax + by = b-a.... (1)$

$\to bx - ay = -(a+b)....(2)$

Let us eliminate the variable 'y'. To do so, firstly multiply (1) by 'a' and (2) by 'b'. The equations become:

$\to a^2x + aby = a(b-a).... (3)$

$\to b^2x - aby = -b(a+b)....(4)$

Secondly add (3) and (4),

$\to a^2x + b^2x = a(b-a)-b(a+b)$

$\to (a^2 + b^2)x = ab-a^2-ab - b^2$

$\to (a^2 + b^2)x = -a^2- b^2$

$\to (a^2 + b^2)x = -(a^2 + b^2)$

$\to x = -1$, a, b ≠ 0.

Substituting $x = - 1$ in (1),we get

$\to a(-1) + by = b-a$

$\to by = b - a + a$

$\to by = b$

$\to y = 1$, b ≠ 0.

Thus, $x = - 1,\:y = 1$