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ANTONII [103]
3 years ago
12

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) = ( ________ ) ...?
Mathematics
2 answers:
d1i1m1o1n [39]3 years ago
8 0

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 = 4\times \frac{92}{23}-18=-2

y = (-2)+ 2\frac{92}{23} -1=5

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

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

ad-work [718]3 years ago
5 0
<span>x − y + 2z = 1
3x + y + 5z = 19
2x − y − 2z = −17

-3x+3y-6z=-3
</span>3x + y + 5z = 19

4y-z=16 (1)

-2x+2y-4z=-2
<span>2x − y − 2z = −17

y-6z=-19  (2)

</span>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

<span>x − y + 2z = 1
</span>x-5+2×4=1
x-5+8=1
x+3=1
x=-2

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