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The solution to the system of equations is x = 1, y = 10 and z = 4
The system of equations is given as:
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
Multiply the second equation by 2
So, we have
4x - 2y + 6z = 8
Add this equation to the first equation
3x + 4x + 2y - 2y + 4z + 6z = 11 + 8
Evaluate the like terms
7x + 10z = 19
Multiply the second equation by 3
So, we have
6x - 3y + 9z = 12
Subtract this equation from the third equation
6x - 5x - 3y + 3y + 9z - 5z = 12 + 1
Evaluate the like terms
x + 4z = 13
Make x the subject
x = 13 - 4z
Substitute x = 13 - 4z in 7x + 10z = 19
7(13 - 4z) + 10z = 19
Expand
91 - 28z + 10z = 19
Evaluate the like terms
-18z = -72
Divide
z = 4
Substitute z = 4 in x = 13 - 4z
x = 13 - 4 * 4
Evaluate
x = 1
We have:
2x -y +3z = 4
This gives
2(1) - y + 3 * 4 = 4
Evaluate
2 - y + 12 = 4
This gives
y = 10
Hence, the solution to the system of equations is x = 1, y = 10 and z = 4
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