x+2y+z=5 To calculate: The solution for the system of equation

Paganellash 2021-11-14 Answered
x+2y+z=5 To calculate: The solution for the system of equation x+yz=1
4x+7y+2z=16
and if the system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
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Expert Answer

Edward Belanger
Answered 2021-11-15 Author has 11 answers
Calculation:
Consider the provided system of equations is,
x+2y+z=5......(1)
x+yz=1......(2)
4x+7y+2z=16......(3)
Now, add both the equations (1) and (2).
x+x+2y+y+zz=5+1
......(3) 2x+3y=6
Consider the second and third equation from (1),
x+yz=1
......(4) 4x+7y+2z=16
Multiply the equation (1) by 2 and add with equation (3).
2x+4x+2y+7y2z+2z=2+16
......(7) 6x+9y=18
Multiply the equation (3) with —3 and with equation (7).
6x+6x+9y9y=18+18
0=0
The system reduces to the identity 0=0.
So, the system has infinitely many solutions.
6x=245y Therefore, the system of equations 14=7z3y has infinitely many
4x3z=10 solutions.
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