if ;X+y=8;
X+z=13
z-w=6
y+w=8
then find w;X;y;z
Answers
Answer:
w:x:y:z =7:7:9:19
Step-by-step explanation:
x+y=8----(i)
x+z=13----(ii)
z-w=6----(iii)
y+w=8----(iv)
adding these 4 equation ,
2(x+y+z)=35
∴(x+y+z)=35/2----(v)
subtracting (i) & (v) ,we get--
z=19/2;
x=7/2;
y=9/2;
w=7/2.
∴ w:x:y:z =7:7:9:19
Step-by-step explanation:
Given:-
X+y=8
X+z=13
z-w=6
y+w=8
To find:-
Find W,X,Y and Z ?
Solution:-
Given that
X+y=8 ----(1)
X+z=13----(2)
z-w=6-----(3)
y+w=8-----(4)
On subtracting (1) from (2)
X+ Z = 13
X+Y = 8
(-)
_______
0+Z-Y = 5
________
Z-Y = 5 -------(5)
On subtracting (5) from (3)
Z-W = 6
Z-Y = 5
(-)
_______
0+Y-W = 1
________
Y-W = 1---------(6)
On adding (6)& (4)
Y+W = 8
Y-W = 1
(+)
________
2Y +0 = 9
________
=> 2Y = 9
=> Y = 9/2
The value of Y = 9/2
On Substituting the value of Y in (6)
(9/2)-W = 1
=> W = (9/2)-1
=> W = (9-2)/2
=> W = 7/2
The value of W = 7/2
Substituting the value of Y in (1)
=> X + (9/2) = 8
=>X = 8-(9/2)
=>X = (16-9)/2
=> X = 7/2
The value of X = 7/2
On Substituting the value of X in (2)
=> (7/2)+Z = 13
=> Z = 13-(7/2)
=> Z = (26-7)/2
=> Z = 19/2
The value of Z = 19/2
Answer:-
The values of the variables :
X = 7/2 ; Y = 9/2 ; W = 7/2 ; Z = 19/2
Check:-
X+y=8
(7/2)+(9/2)
=> (7+9)/2
=> 16/2
=> 8
X+z=13
(7/2)+(19/2)
=> (7+19)/2
=> 26/2
=> 13
z-w=6
=>(19/2)-(7/2)
=> (19-7)/2
=> 12/2
=>6
y+w=8
=> (9/2)+(7/2)
=>(9+7)/2
=> 16/2
=> 8
Verified the given relations