The solution to the system of linear equations is x = -9, y =5 and x = 0
How to determine the solution to the system of linear equations?
The system of linear equations is given as:
x + 2y + 3z = 1
2x + 4y + 7z = 2
3x + 7y + 11z = 8
Multiply the equation x + 2y + 3z = 1 by 2.
So, we have:
2x + 4y + 6z = 2
Subtract 2x + 4y + 6z = 2 from 2x + 4y + 7z = 2
So, we have:
2x - 2x + 4y - 4y + 7z - 6z = 2 - 2
Evaluate the like terms
z = 0
Substitute z = 0 in the equations.
So, we have:
2x + 4y = 2
3x + 7y = 8
Multiply 2x + 4y = 2 by 3 and 3x + 7y = 8 by 2
So, we have:
6x + 12y = 6
6x + 14y = 16
Subtract the equations
-2y = -10
Divide by -2
y = 5
Substitute y = 5 in 3x + 7y = 8
3x + 7 * 5 = 8
This gives
3x = 8 - 35
So, we have
3x = -27
Divide by 3
x = -9
Hence, the solution to the system of linear equations is x = -9, y =5 and x = 0
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