Answer:
A) No solution.
B) -2, 1, 2
C) 2, 1, - 2
D) Infinite number of solutions
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