See the attachment for the problem

A) No solution.

B) -2, 1, 2

C) 2, 1, - 2

D) Infinite number of solutions

Step-by-step explanation:

A) 2x + 5y - z = -2

3x - 2y + z = 4

-x + 7y - 2z = 2

Let's add eq(1) and eq(2) to eliminate z.

2x + 3x + 5y - 2y - z + z = -2 + 4

5x + 3y = 2 - - - (eq 4)

Let's multiply eq(2) by 2 and add to eq(3) to eliminate z.

6x - x - 4y + 7y + 2z - 2z = 8 + 2

5x + 3y = 6 - - -(eq 5)

Subtracting eq(4) from eq(5) gives;

0 = 4

This is inconsistent and thus the system of equation has no solution.

B) 4x + 5y + 3z = 3

-3x + 4y - z = 8

5x + 3y + 2z = -3

Multiply eq 2 by 3 and add to eq 1 to eliminate z;

4x - 9x + 5y + 12y + 3z - 3z = 3 + 24

-5x + 17y = 27 - - - (eq 4)

Multiply eq 2 by 2 and add to eq 3 to eliminate z;

5x - 6x + 3y + 8y + 2z - 2z = -3 + 16

-x + 11y = 13 - - - (eq 5)

Multiply eq (5) by -5 and add to eq 4 to get;

17y - 55y = 27 - 65

-38y = - 38

y = 1

Putting 1 for y in eq 5 gives; x = -2

Putting x = - 2 and y = 1 in eq 1 gives;

z = 2

C) 4x - 3y + 2z = 1

-2x + 3y - 2z = 3

2x - 3y + 3z = -5

Solving this equation simultaneously via a calculator gives;

x = 2, y = 1, z = - 2

D) 2x + 3y - z = -2

x - 9y + 2z = 8

-x - 12y + 3z = 10

Add eq(2) to eq (3) to get;

-21y + 5z = 18 - - - (eq 4)

Multiply eq 2 by 2 and add to eq 3 to get;

-30y + 7z = 26 - - - (eq 5)

From eq 4, z = (18 + 21y)/5

Put this in eq 5 to get;

-30y + 7(18 + 21y)/5 = 26

-30y + 126/5 + 147y/5 = 26

Solving this leads to infinite number of solutions

1

step-by-step explanation:

it's the only multiple of both and the least

fd

step-by-step explanation: