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.

Paganellash
2021-11-14
Answered

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.

You can still ask an expert for help

Edward Belanger

Answered 2021-11-15
Author has **11** answers

Calculation:

Consider the provided system of equations is,

$x+2y+z=5$ ......(1)

$x+y-z=1$ ......(2)

$4x+7y+2z=16$ ......(3)

Now, add both the equations (1) and (2).

$x+x+2y+y+z-z=5+1$

......(3)$2x+3y=6$

Consider the second and third equation from (1),

$x+y-z=1$

......(4)$4x+7y+2z=16$

Multiply the equation (1) by 2 and add with equation (3).

$2x+4x+2y+7y-2z+2z=2+16$

......(7)$6x+9y=18$

Multiply the equation (3) with —3 and with equation (7).

$-6x+6x+9y\u20149y=-18+18$

$0=0$

The system reduces to the identity$0=0$ .

So, the system has infinitely many solutions.

$6x=24\u20145y$
Therefore, the system of equations $14=7z\u20143y$ has infinitely many

$4x\u20143z=10$
solutions.

Consider the provided system of equations is,

Now, add both the equations (1) and (2).

......(3)

Consider the second and third equation from (1),

......(4)

Multiply the equation (1) by 2 and add with equation (3).

......(7)

Multiply the equation (3) with —3 and with equation (7).

The system reduces to the identity

So, the system has infinitely many solutions.

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