Question

Solve : x + y = 18; y + z = 12; z + x = 16

Answer 1

EXPLANATION.

⇒ x + y = 18. ⇒ (1)

⇒ y + z = 12. ⇒(2)

⇒ z + x = 16. ⇒(3)

As we know that,

From equation (1), we get.

⇒ x = 18 - y. ⇒ (4).

From equation (2), we get.

⇒ z = 12 - y. ⇒(5).

Put the value of equation (4) & (5) in equation (3), we get.

⇒ (12 - y) + (18 - y) = 16.

⇒ 12 - y + 18 - y = 16.

⇒ 30 - 2y = 16.

⇒ -2y = 16 - 30.

⇒ -2y = -14.

⇒ y = 7.

Put the value of y = 7 in equation (4), we get.

⇒ x = 18 - y.

⇒ x = 18 - 7.

⇒ x = 11.

Put the value of y = 7 in equation (5), we get.

⇒ z = 12 - y.

⇒ z = 12 - 7.

⇒ z = 5.

Values of x = 11 & y = 7 & z = 5.

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

$\tt \: x + y = 18 - - - (1)$

$\tt \: y + z = 12 - - - (2)$

$\tt \: z + x = 16 - - - (3)$

On adding equation (1), (2) and (3), we get

$\rm :\implies\:2(x + y + z) = 46$

$\rm :\implies\: x + y + z = 23 - - - (4)$

On Subtracting equation (1) from (4), we get

$\rm :\implies\:x + y + z - x - y = 23 - 18$

$\rm :\implies\: \boxed{ \red{ \bf \: z = 5}}$

On Subtracting equation (2) from (4), we get

$\rm :\implies\:x + y + z - y - z = 23 - 12$

$\rm :\implies\: \boxed{ \green{ \bf \: x = 11}}$

On Subtracting equation (3) from (4), we get

$\rm :\implies\:x + y + z - z - x = 23 - 16$

$\rm :\implies\: \boxed{ \purple{ \bf \: y = 7}}$