if 2x + 3y =31,y - z =4 and x + 2y = 11 then find the value of x+y+z.
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the ans is 8 and x=29 y=-9 abd z= -13
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2x + 3y = 31 . . . .(i);
y - z = 4 . . . (ii)
and x + 2z = 11 . . . .(iii)
Multiplying (iii) by 2 and subtracting from (i),
we get : 3y - 4z = 9 . . . .(iv)
Solving (ii) and (iv),
we get : y =7, z = 3.
Putting y = 7 in (i), we get :x = 5.
∴
x + y + z = (5 + 7 + 3) = 15.
y - z = 4 . . . (ii)
and x + 2z = 11 . . . .(iii)
Multiplying (iii) by 2 and subtracting from (i),
we get : 3y - 4z = 9 . . . .(iv)
Solving (ii) and (iv),
we get : y =7, z = 3.
Putting y = 7 in (i), we get :x = 5.
∴
x + y + z = (5 + 7 + 3) = 15.
pihu983:
thank you
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