Question

Solve the following system of equations for the given variables.
(1) x+y= 7;
(ii)x-y = - 1

(2) 2x + y = 8;
(ii)x-2y = -1

(3) 4x + 3y = 5;
(ii)2x-y = 2
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Answer 1

Answer:

x+y+xy=5...(i)

x2+y2+xy=7...(ii)

we know that a2+b2+2ab=(a+b)2

Simplifying equation (ii)

x2+y2+xy=7

or, x2+y2+2xy−xy=7

or, (x+y)2−xy=7...(iii)

Simplifying equation (i)

x+y+xy=5

or, x+y=5−xy...(iv)

Putting this value of (x+y) in equation (iii)

(5−xy)2−xy=7

or, 25+x2y2−10xy−xy=7

or, x2y2−11xy+25−7=0

or x2y2−11xy+18=0

or, x2y2−2×xy×211