Question

{3x+4y-z=-7
X-5y+2z=19
5x+y-2z=5

Answer 1

x = 2, y = -3 and z = 1.

Explanation:

3x+4y-z=-7 ............. A

X-5y+2z=19 ..............B

5x+y-2z=5 ...............C

Adding equations B and C to eliminate z:

6x - 4y + 0 = 24

6x - 4y = 24.............D

Now we multiply Equation A by 2:-

6x + 8y - 2z = -14

Now adding this to equation B, ( again to eliminate z) we get equation E:

7x + 3y = 5 -----------E

Bring down equation D:

6x - 4y = 24.............D

Multiplying E by 4 and D by 3:

28x + 12y = 20

18x - 12y = 72

Adding:

46x = 92

x = 2.

and substituting in equation D

6(2)- 4y = 24

-4y = 12

y = -3.

Finally we find z by substituting in equation A:

3(2) + 4(-3) - z = -7

-z = -7 - 6 + 12

-z = -1

z = 1.