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Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.)


x − y + 2z = 1
3x + y + 5z = 19
2x − y − 2z = −17
(x, y, z) = ( ________ ) ...?

Respuesta :

x − y + 2z = 1
3x + y + 5z = 19
2x − y − 2z = −17

-3x+3y-6z=-3
3x + y + 5z = 19

4y-z=16 (1)

-2x+2y-4z=-2
2x − y − 2z = −17

y-6z=-19  (2)

4y-z=16  (1)
y-6z=-19 (2)

4y-z=16 
-4y+24z=76

23z=92
z=4

y-6z=-19
y-6×4=-19
y-24=-19
y=24-19
y=5

x − y + 2z = 1
x-5+2×4=1
x-5+8=1
x+3=1
x=-2

(x,y,z)=(-2,5,4)

Answer:

The solution of equation is :(-2,5,4)

Step-by-step explanation:

x - y + 2z = 1

..[1]

3x + y + 5z = 19  ..[2]

2x - y - 2z = -17 ...[3]

Putting value of y from [1] in [2]and [3]

y = x+ 2z -1

3x + (x+ 2z -1) + 5z = 19  

4x + 7z = 20  ...[4]

2x - (x+ 2z -1) - 2z = -17

x - 4z = -18   ...[5]

Solving equation [4] and [5] by substitution:

Putting values of x from [5] in [4]

x = 4z -18

4(4z -18) + 7z = 20  ...[4]

16z - 72+ 7z =20

23z = 92

z = 4

x = [tex]4\times \frac{92}{23}-18=-2[/tex]

[tex]y = (-2)+ 2\frac{92}{23} -1=5[/tex]

(x,y,z)= (5.-2,4)

The solution of equation is :(-2,5,4)

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