the following:
10 12
(ii) Х
11 13
10 12
(vi) X
11 14
please help
Answers
Answer:
Step-by-step explanation:
SOLUTION:
FROM Equation+2:
X + Y = 4
Y = 4-X --> Equation+4
MULTIPLY Equation+1 WITH -1 AND ADD TO Equation+3 TO ELIMINATE Z:
-X -2Y - Z = -6 --> Equation+5
ADD Equation+5 AND Equation+3:
-X -2Y - Z = -6 --> Equation+5
3X + Y + Z = 8 --> Equation+3
_______________
2X -Y = 2
2X -Y = 2 --> Equation+6
NOW WE CAN SOLVE FOR X USING Equation+4 AND Equation+6 BY SUBSTITUTION:
2X -Y = 2 --> Equation+6
2X -(4-X) = 2
2X -4 + X = 2
3X = 2 + 4
3X = 6
X = 6/3
X+=+2
NOW THAT WE HAVE X, WE CAN SOLVE FOR Y USING Equation+2 AND X=2 BY SUBSTITUTION:
X + Y = 4 --> Equation+2
2 + Y = 4
Y = 4-2
Y+=+2
NOW THAT WE HAVE x AND Y, WE CAN SOLVE FOR Z USING Equation+1 BY SUBSTITUTION:
X + 2Y + Z = 6 --> Equation+1
2 + 2(2) + Z = 6
2 + 4 + Z = 6
6 + Z = 6
Z = 6-6
Z+=+0
ANSWER+TO+PROBLEM+A
X+=+2
Y+=+2
Z+=+O
PROBLEM B.
GIVEN:
10X + Y + Z = 12 --> Equation+1
8X + 2Y + Z = 11 --> Equation+2
20X - 10Y - 2Z = 8 --> Equation+3
REQUIRED: FIND X, Y AND Z
SOLUTION:
MULTIPLY Equation+1 WITH -1 AND ADD TO Equation+2 TO ELIMINATE Z:
-10X - Y -Z = -12 --> Equation+1*(-1)
8X +2Y +Z = 11 --> Equation+2
_________________
-2X + Y = -1
-2X + Y = -1 --> Equation+4
FROM Equation+4:
-2X + Y = -1 --> Equation+4
Y = 2X-1 --> Equation+5
NOW MULTIPLY Equation+2 WITH 2 AND ADD TO Equation+3 TO ELIMINATE Z:
16X + 4Y + 2Z = 22 --> Equation+2*(2)
20X - 10Y - 2Z = 8 --> Equation+3
___________________
36X - 6Y = 30
36X - 6Y = 30 --> Equation+6
NOW WE CAN SOLVE FOR X USING Equation+5 IN Equation+6:
36X - 6Y = 30 --> Equation+6
36X - 6(2X-1) = 30
36X -12X + 6 = 30
24X = 30-6
24X = 24
X = 24/24
X+=+1
NOW THAT HAVE HAVE X, WE CAN SOLVE FOR Y USING Equation+5:
Y = 2X -1 --> Equation+5
Y = 2(1)-1
Y = 2 - 1
Y+=+1
NOW THAT HAVE HAVE X AND Y, WE CAN SOLVE FOR Z USING Equation+1, Equation+2 OR Equation+%0D%0A%0D%0A3, LETS TRY Equation+1:
10X + Y + Z = 12 --> Equation+1
10(1) + 1 + Z = 12
10 + 1 + Z = 12
11 + Z = 12
Z = 12-11
Z+=+1
ANSWER+TO+PROBLEM+B
X+=+1
Y+=+1
Z+=+1
PROBLEM C
GIVEN:
22X + 5Y + 7Z = 12 --> Equation+1
10X + 3Y + 2Z = 5 --> Equation+2
9X + 2Y + 12Z = 14 --> Equation+3
REQUIRED: FIND X, Y AND Z
SOLUTION:
MULTIPLY Equation+1 WITH -1 AND ADD TO Equation+2 AND Equation+3 TO ELIMINATE Y:
-22X - 5Y - 7Z = -12 --> Equation+1*(-1)
10X + 3Y + 2Z = 5 --> Equation+2
9X + 2Y + 12Z = 14 --> Equation+3
____________________
-3X + 7Z = 7
-3X + 7Z = 7 --> Equation+4
FROM Equation+4:
-3X + 7Z = 7 --> Equation+4
3X = 7Z - 7
X = (7Z -7)/3 --> Equation+5
MULTIPLY Equation+3 WITH -%283%2F2%29 AND ADD TO Equation+2 TO ELIMINATE Y:
-(27/2)x - 3Y - 18z = -21 --> Equation+3 * (-3/2)
10X + 3Y + 2Z = 5 --> Equation+2
_________________________
(-7/2)x - 16z = -16
(-7/2)x - 16z = -16 --> Equation+7
FROM Equation+7:
[(-7/2)x - 16z = -16] * 2 --> Equation+7*2
-7X - 32Z = -32 --> Equation+8
NOW WE CAN SOLVE FOR X USING Equation+5 IN Equation+8:
7X - 32Z = -32 --> Equation+8
-7[(7Z-7)/3] - 32Z = -32
[(-49Z + 49)/3 - 32Z = -32] *3
-49Z + 49 - 96Z = -96
-145Z = -145
Z = -145/-145
Z+=+1
NOW THAT WE HAVE Z WE CAN SOLVE FOR X USING Equation+5:
X = (7Z -7)/3 --> Equation+5
X = [7(1) - 7]/3
X = (7-7)/3
X = 0/3
X+=+0
NOW THAT HAVE HAVE Z AND Y, WE CAN SOLVE FOR Y USING Equation+1, Equation+2 OR Equation+%0D%0A%0D%0A3, LETS TRY Equation+1:
22X + 5Y + 7Z = 12 --> Equation+1
22(0) + 5Y + 7(1) = 12
0 + 5Y + 7 = 12
5Y = 12-7
5Y = 5
Y = 5/5
Y+=+1
ANSWER+TO+PROBLEM+C
X+=+0
Y+=+1
Z+=+1