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Solve the system of equations. If a 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.
- 2x + 6y + 3: = -31
- 3y + 7: = 59
2- = 10
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6
The system has one solution.
The solution set is {C10}
The system has no solution.
The system is inconsistent.
The equations are dependent.
The system has infinitely many solutions
The system is inconsistent
The equations are dependent
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Solve the system of equations If a system has one unique solution write the solution set Otherwise determine the number of solutions to the system and determine class=

Respuesta :

The value of x, y and z from the system of equation are -1, -8 and 5 respectively.

Data;

  • -2x + 6y + 3z = -31
  • -3y + 7z = 59
  • 2z = 10

System of Equation

To solve this problem, we have to solve the system of equation using substitution method.

From equation (iii)

[tex]2z = 10\\z = 5[/tex]

let us substitute the value of z into equation (ii)

[tex]-3y + 7z = 59\\z = 5\\-3y + 7(5) = 59\\-3y + 35 = 59\\-3y = 59 - 35\\-3y = 24\\y = -8[/tex]

Let's substitute the value of x and y into equation (i)

[tex]-2x + 6y + 3z = -31\\y = -8, z = 5\\-2x + 6(-8) + 3(5) = -31\\-2x - 48 + 15 = -31\\-2x - 33 = -31\\-2x = -31 + 33\\-2x = 2\\x = -1[/tex]

From the calculation above, the value of x, y and z are -1, -8 and 5 respectively.

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