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