What is a+b=2,a+c=3,b+c=4 ?

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

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a+b=2,a+c=3,b+c=4

a + b = 2, a + c = 3, b + c = 4

a = \frac{1}{2}, b = \frac{3}{2}, c = \frac{5}{2}

Solution steps

a + b = 2 a + c = 3 b + c = 4

Isolate

a

for

a + b = 2 : a = 2 - b

Substitute

a = 2 - b

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

Isolate

b

for

2 - b + c = 3 : b = c - 1

Substitute

b = c - 1

[c - 1 + c = 4]

Simplify

[2 c - 1 = 4]

Isolate

c

for

2 c - 1 = 4 : c = \frac{5}{2}

For

b = c - 1

Substitute

c = \frac{5}{2}

b = \frac{5}{2} - 1

\frac{5}{2} - 1 = \frac{3}{2}

b = \frac{3}{2}

For

a = 2 - b

Substitute

b = \frac{3}{2}, c = \frac{5}{2}

a = 2 - \frac{3}{2}

2 - \frac{3}{2} = \frac{1}{2}

a = \frac{1}{2}

The solutions to the system of equations are:

a = \frac{1}{2}, b = \frac{3}{2}, c = \frac{5}{2}

5 x + 2 y = 10, - 3 x + 3 y = 5

x + 4 y = - 4, 3 y - 5 x = - 1

7 x - 6 y = 12, 5 x + 3 y = 11

x + y = 4, 5 x - y = 21

x + 2 y = 1, - x - y = 2

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