Question

If 3x+y-3z=11 and 2x-2z+5y=29 what is the value of x+y-z?

Answer 1

Hello,
3x+y-3z=11          (1)
2x-2z+5y=29        (2)

Multiply (1) by a factor 2 and (2)by a factor of 3:

6x + 2y - 6z = 22      (3)

6x + 15y - 6z = 87    (4)

Subtract (3) from (4)

6x + 15y - 6z - (6x + 2y - 6z) = 87 - 22

or

6x - 6x + 15y - 2y - 6z + 6z = 65

or

13y = 65

y=65:13=5

and therefore

 y = 5

 

 

Look at (1).

wWe can rewrite this as

3(x - z) + y = 11

we know y = 5 and there fore (1) can be rewritten as

3(x - z) + 5 = 11

or 

3(x - z) = (11 - 5)

3(x - z) = 6

(x - z) = 6/3=2

(x - z) = 2

 

So lets add up (x - z) and y:

(x - z) + y = 2 + 5

or 

x + y - z = 7

bye :-)

Answer 2

Answer:

7

Step-by-step explanation:

Let x-z=m

So,

3m + y = 11        ------(1)

2m + 5y = 29   ------(2)

Multiply (1) by 5 and then substract it by (2)

15m - 2m = 26 => 13m = 26 => m = 2

Put m = 2 in (1) => 6 + y = 11 => y = 5

x + y - z = m + y = 2 + 5 = 7