What is x+y+3z=1,2x+y+2z=3,3x+2y+5z=3 ?

The solution to x+y+3z=1,2x+y+2z=3,3x+2y+5z=3 is No Solution

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

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

No Solution

Solution steps

x + y + 3 z = 1 2 x + y + 2 z = 3 3 x + 2 y + 5 z = 3

Isolate

x

for

x + y + 3 z = 1 : x = 1 - y - 3 z

Substitute

x = 1 - y - 3 z

[2 (1 - y - 3 z) + y + 2 z = 3 3 (1 - y - 3 z) + 2 y + 5 z = 3]

Simplify

[- y - 4 z + 2 = 3 - y - 4 z + 3 = 3]

Isolate

y

for

- y - 4 z + 2 = 3 : y = - 4 z - 1

Substitute

y = - 4 z - 1

[- (- 4 z - 1) - 4 z + 3 = 3]

Simplify

[4 = 3]

4 = 3

is false, therefore the system of equations has no solution

No Solution

35 x - 30 y + 12 = 0, 30 x + 35 y - 10 = 0

3 x - 4 y + 24 = 0, x + y - 13 = 0

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

3 x + y = 3, 4 x - 3 y = 17

3 x + 2 y + z = 1, 5 x + 3 y + 4 z = 2, x + y - z = 1

What is x+y+3z=1,2x+y+2z=3,3x+2y+5z=3 ?
The solution to x+y+3z=1,2x+y+2z=3,3x+2y+5z=3 is No Solution