Question

Take 70 as the assumed mean. Find mean up to two places of d
(ii) Solve the following simultaneous equations for x and y.
m(x + y) + n(x - y) - (m2 + mn + n2) = 0;
n(x + y) + m(x - y) = (m - mn + n) = 0.
(1) Let x + y = a, x-y= b.
(2) Transfer the terms not containing x and y to RHS.
(3) Add equations, substitute the values of a and b and solve.
QUESTION PAPERS FOR PRACTICE : MATHEMATICS (PAR​

Answer 1

Step-by-step explanation:

let x+y be a and x-y be b

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqn

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)(a+b)(m+n)=2(m²-n²)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)(a+b)(m+n)=2(m²-n²)x+y+x-y (m+n)=2(m²-n²)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)(a+b)(m+n)=2(m²-n²)x+y+x-y (m+n)=2(m²-n²)2x(m+n)=2(m²-n²)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)(a+b)(m+n)=2(m²-n²)x+y+x-y (m+n)=2(m²-n²)2x(m+n)=2(m²-n²) x=(m²-n²)/(m+n)

let x+y be a and x-y be bma+nb-m²+mn-n² (opening the bracket)na+mb=m²-mn+n ....1same with another equation we get,na+mb=m²-mn-n²....2adding both the eqnma+nb+na+mb=m²+mn-n²+m²-mn-n²ma+mb+na+nb=2m²-2n²m(a+b)+n(a+b)=2(m²-n²)(a+b)(m+n)=2(m²-n²)x+y+x-y (m+n)=2(m²-n²)2x(m+n)=2(m²-n²) x=(m²-n²)/(m+n)mimilarly we can find y