What is a+b=3,b+c=4,c+a=5 ?

The solution to a+b=3,b+c=4,c+a=5 is a=2,b=1,c=3

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a+b=3,b+c=4,c+a=5

a + b = 3, b + c = 4, c + a = 5

a = 2, b = 1, c = 3

Solution steps

a + b = 3 b + c = 4 c + a = 5

Isolate

a

for

a + b = 3 : a = 3 - b

Substitute

a = 3 - b

[b + c = 4 c + 3 - b = 5]

Isolate

b

for

b + c = 4 : b = 4 - c

Substitute

b = 4 - c

[c + 3 - (4 - c) = 5]

Simplify

[2 c - 1 = 5]

Isolate

c

for

2 c - 1 = 5 : c = 3

For

b = 4 - c

Substitute

c = 3

b = 4 - 3

Simplify

b = 1

For

a = 3 - b

Substitute

b = 1, c = 3

a = 3 - 1

Simplify

a = 2

The solutions to the system of equations are:

a = 2, b = 1, c = 3

2 x - 3 y = - 16, 5 x + 3 y = 2

9 x - 4 y = 23, 2 x - y = 12

10 x + 8 y + z = 20, 0 x + y + z = 100

3 x + 4 y + 10 = 0, x - y = 2

2 x + 3 y = 20, x - 2 y = 3