Question

If x=a y=b is the solution of the pair of equations x - y=2 and x +y=4 then respective values of a and b are ​

Answer 1

Question :

If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=5 then respective values of a and b are.

To find :

That values of x and y=?

Solution :

$\\ \implies \bf \: x - y = 2 \: \: \: \: \: \: ...equation (1)$

$\\ \implies \bf\: x + y = 4 \: \: \: \: \: .....equation \: (2)$

$\bf{ \underline{ \diamondsuit \: \: adding \: both \: equations \: (1) \: and \: (2)}}$

$\\ \implies \sf \: x - y = 2$

$\implies \sf \: x + y = 4$

(+) (-)

______________________

$\\ \implies \sf \: 2x = 2 + 4$

$\implies \sf \: 2x = 6$

$\\ \implies \sf \: x = \frac{6}{2} = 3$

$\implies \boxed{ \sf{ \: x = 3}}$

$\bf{ \underline{ \diamondsuit \: put \: x = 3 \: in \: equation \: (1) \: or \: (2)}}$

$\implies \sf \: x - y = 2$

$\implies \sf \: 3 - y - 2 = 0$

$\implies \sf \: - y - 1 = 0$

$\implies \sf \: y = - 1$

$\implies \boxed{ \sf{y = - 1}}$

$\therefore \boxed{ \sf{ \: x = a \: \: ie \to \: a = 3}}$

$\therefore\boxed{ \sf{ \: y = b \: ie \to \: b = - 1}}$