Question

A+B=8
C-D=6
A+C=13
B+D=8​

Answer 1

Answer:

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A + B = 8 ----(1)

C - D = 6 ----(2)

A + C = 13 ----(3)

B + D = 8 ---(4)

equating eq (1) and eq (4)

A + B = B + D

A = D ----(5)

substituting eq (5) in eq ( 2)

C - A = 6

C = 6 + A ---(6)

substituting eq (6) in eq (3)

A + 6 + A = 13

2A = 7

A = 3.5

A = D = 3.5 -----(7)

substituting eq (7) in eq (1)

B = 8 - 3.5

B = 4.5 ----(8)

substituting eq (7) in eq (2)

C - D = 6

C = 6 + 3.5

C = 9.5

Verification

A + B = 8

+ +

C - D = 6

|| ||

13 8

3.5 + 4.5 = 8

+ +

9.5 - 3.5

|| ||

13 8

A = 3.5 , D = 3.5 , B = 4.5 , C = 9.5

Answer 2

Step-by-step explanation:

Given a + b = 8 ---- (1)

a + c = 13  ---- (2)

c - d = 6   ---- (3)

b + d = 8   ---- (4)

On solving 4 equations, we get.

a + b + a + c + c - d + b + d = 35

2a + 2b + 2c = 35

a + b + c = 17.5    ---- (5)

Substitute (1) in (5), we get

8 + c = 17.5

c = 9.5            ----------- (6).

Substitute (6) in (2)

a + 9.5 = 13

a = 3.5           --------------- (7)

Substitute (6) and (7) in (5), we get

3.5 + b + 9.5 = 17.5

b + 13 + 17.5

b = 4.5     -------- (8).

Substitute (8) in (4), we get

4.5 + d = 8

d = 3.5.

The values of a = 3.5,b = 4.5, c = 9.5, d = 3.5.