x+y+z = 7 2x-y+z = 4 Then 11y-10x will be

M4maths Previous Puzzles

24 Apr 2015 Solve Equation

x+y+z = 7
2x-y+z = 4
Then
11y-10x will be

OPtion

1) z
2) 3
3) 2z
4) 5
5) 3z
6) 8
7) 4z
8) 9
9) 5z
10)10

Solution

x+y = 7-z
2x-y = 4-z
On solving x = (11-2z)/3
and y = (10-z)/3
So 11y - 10x = 3z

Option 5)

Correct Option: 5 Best Solution (19)

moumita   9 years AGO

x+y+z=7 & 2x-y+z=4
Solving both the equations, we get, x= (11-2z)/3 & y=(10-z)/3
Now, substituting the value of x and y in the equation (11y-10x) , we get 3z.

Like? Yes (6) | No (5)  

Meenakshi   9 years AGO

x=1,y=2,z=4
11y-10x=12 or 3z

Like? Yes (1) | No   

Abhishek Ranjan   9 years AGO

multiply 4 in equation 1 and multiply 7 in equation 2 and subtract eqn1-eqn2
4x+4y+4z=28
-(14x-7y+4z=28)
11y-10x=3z

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

equating z in both the equation we get
z=7-x-y
z=4-2x+y
7-x-y=4-2x+y
after solving this we get
y=-10/3,x=-29/3
so value of 11y-10x=11*-10/3-10*-29/3=60
=3*z
put the value of x and y in any equatio we get z=20.
11y-10x=3z

Like? Yes (1) | No   

Supriya Mondal   9 years AGO

Here, 2 equations are given and they are
x+y+z=7...................(i)
2x-y+z=4.................(ii)
Now add equation (i) and (ii)
x+y+z+2x-y+z=7+4
so,3x+2z=11
so,x=(11-2z)/3
Now, subtract equation (ii) from 2*equation (i)
2x+2y+2z-2x+y-z=14-4
so,3y+z=10
so,y=(10-z)/3

so, 11y-10x=11*{(10-z)/3} -10*{(11-2z)/3}
=(110-11z)/3 - (110-20z)/3
=(110-11z-110+20z)/3
=9z/3
=3z
So, option 5)3z is the right answer

Like? Yes (1) | No   

ankit kamboj   9 years AGO

by rearranging 2y=x+3 ,, hit and trial x=1,y=2 gives z=4 and it satisfies both the equation so it is a possible solution ,, hence 11y-10x=12=3*z

Like? Yes (1) | No   

Rakesh Kumar Thakur   9 years AGO

Firstly evaluate x & y in terms of z, we get
x=(11-2z)/3
y=(10-z)/3
now substitute the values of x & y in the given equation, we get
3z

Like? Yes (1) | No   

Neha Shahi   9 years AGO

x + y +z =7 ....(i)
2x - y + z =4 .....(ii)
from (i) and (ii) we get : x = (11 - 2z )/3 and y =(10 - z ) /3
putting the value of x and y in 11y - 10 x we get 3z
so option 5 is the correct answer

Like? Yes (1) | No (1)  

kishore   9 years AGO

we can write x+y = 7-z and 2x-y = 4-z make these equations (1) & (2) respt
add (1) & (2) we get x= (11-3z)/3
sub (1) & (2) by multiplying (1) with 2
then we get y= (10-z)/3
calculate 11y-10x we get 3z

Like? Yes (1) | No (1)  

umesh   9 years AGO

x+y+z=7.....1
2x-y+z=4....2
solve eq 1&2 we get 3x+2z=11.....3
put x=7-y-z
in eq 2 we get z-3y=10.....eq....4
solve eq 2&4
we get 3x+z=1...5
now solve eq 3&5 we get z=10,x=-3,y=0
put the value ans will be 3z

Like? Yes (1) | No (1)  

Srinivas   9 years AGO

on solving -x + 2y = 3
and 3y+z = 10
so -10x+11y = 3z

Like? Yes (1) | No (1)  

santosh kumar patel   9 years AGO

(x+y+z = 7) put x=1, y=2 and z=4
2x-y+z = 4 satisfy the abobe equations
so
11y-10x=3z

Like? Yes (2) | No (2)  

shreya saklecha   9 years AGO

we can write the given equation as:
x+y-7=-z
2x-y-4=-z
on soving both equations we get:
x=1/3(11-2z) y=1/3(-z+10)
putting this values of x &y in given equation:
ans. 3z

Like? Yes (2) | No (2)  

shaik sharina   9 years AGO

3x+2z=11
x=[11-2z]/3
y=10-z/3
11y-10x=3z

Like? Yes (2) | No (2)  

ANUJ KUMAR   9 years AGO

From given equations eliminating y variable we get:
3x+2z=11
solve for x we get:
x=(11-2z)/3
Now substitute x in any given equation say x+y+z=7 and solve for y we get:
y=(10-z)/3
Now put values of x and y in required equation 11y-10x we get
11*(10-z)/3-10*(11-2z)/3=3z

Like? Yes (1) | No (2)  

Jaspalsingh Parmar   9 years AGO

by solving by trial and error method
we get x=1,y=2,z=4
so
11*2 - 10*1 = 12
means 3*z=3*4 =12

Like? Yes (2) | No (3)  

poojasaisri   9 years AGO

given eqns 1+2=> 3x+2z=11 =>x=(11-2z)/3
substituting x in eqn 1 gives y=(10-z)/3
substituting x and y in 11y-10x =3z

Like? Yes (1) | No (2)  

siddharth prakash singh   9 years AGO

since x+y+z = 7
so, x=7-y-z
and since 2x-y+z = 4
so, y=2x+z-4
Therefore, 11y-10x= 11(2x+z-4) - 10(7-y-z)
=22x+11z-44-70+10y+10z
=22x+10y+21z-114
Also on solving both the given equation we get y=(10-z)/3 and x= 2y-3. so on putting the value of x and y we get,
required value as 3z

Like? Yes (1) | No (2)  

Anuradha   9 years AGO

Solve in matrix form:(calculating determinant)
x/(1+1)=-y/(1-2)=z/(-1-2)
=> x/2=y/1=z/-3
(i.e x=2,y=1,z=-3)

11y=11*1=11
10x=10*2=20
=> 11y-10x=11-20=-9
z=-3
=> 3z=-9
=>11y-10x=-9=3z

Like? Yes (1) | No (3)