What is a+2b-c=-3,3a+b+c=4,a-b+2c=6 ?

The solution to a+2b-c=-3,3a+b+c=4,a-b+2c=6 is a=1,b=-1,c=2

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a+2b-c=-3,3a+b+c=4,a-b+2c=6

a + 2 b - c = - 3, 3 a + b + c = 4, a - b + 2 c = 6

a = 1, b = - 1, c = 2

Solution steps

a + 2 b - c = - 3 3 a + b + c = 4 a - b + 2 c = 6

Isolate

a

for

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

Substitute

a = - 3 - 2 b + c

[3 (- 3 - 2 b + c) + b + c = 4 - 3 - 2 b + c - b + 2 c = 6]

Simplify

[- 5 b + 4 c - 9 = 4 - 3 b + 3 c - 3 = 6]

Isolate

b

for

- 5 b + 4 c - 9 = 4 : b = - \frac{- 4 c + 13}{5}

Substitute

b = - \frac{- 4 c + 13}{5}

[- 3 (- \frac{- 4 c + 13}{5}) + 3 c - 3 = 6]

Simplify

[\frac{3 c + 39}{5} - 3 = 6]

Isolate

c

for

\frac{3 c + 39}{5} - 3 = 6 : c = 2

For

b = - \frac{- 4 c + 13}{5}

Substitute

c = 2

b = - \frac{- 4 \cdot 2 + 13}{5}

Simplify

b = - 1

For

a = - 3 - 2 b + c

Substitute

b = - 1, c = 2

a = - 3 - 2 (- 1) + 2

- 3 - 2 (- 1) + 2 = 1

a = 1

The solutions to the system of equations are:

a = 1, b = - 1, c = 2

x + 7 - 6 x - 2 y = - 4, y = 2

4 x - 2 y = 8, - x + y = 6

3 x + 2 y + 6 z = 24, 2 x + 4 y + 3 z = 23, 5 x + 3 y + 4 z = 33

x + 6 y = 7, 2 x + y = 3

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

What is a+2b-c=-3,3a+b+c=4,a-b+2c=6 ?
The solution to a+2b-c=-3,3a+b+c=4,a-b+2c=6 is a=1,b=-1,c=2