Linear Equation in 2 variables

Algebra Level 1

Sum of 2 number is 35 and difference is 13 Find the numbers and select their product.

360 264 None of these 121

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4 solutions

Hassan Raza
Aug 2, 2014

L e t " x " a n d " y " b e t w o n u m b e r s T h e n S u m x + y = 35 . . . . . . . . . . . . . . . ( i ) D i f . x y = 13 . . . . . . . . . . . . . . . ( i i ) B y a d d i n g ( i ) & ( i i ) , w e h a v e 2 x = 48 o r x = 24 F r o m ( i ) y = 11 P r o d u c t x y = ( 24 ) ( 11 ) t h u s a n s w e r i s 264 Let\quad "x"\quad and\quad "y"\quad be\quad two\quad numbers\\ Then\\ Sum\qquad x+y=35\quad ...............\quad (i)\\ Dif.\qquad x-y=13\quad ...............\quad (ii)\\ By\quad adding\quad (i)\quad \& \quad (ii),\quad we\quad have\\ \qquad 2x=48\\ or\quad \boxed { x=24 } \\ \qquad From\quad (i)\quad \boxed { y=11 } \\ Product\\ \qquad xy=\quad (24)(11)\\ thus\quad answer\quad is\quad \boxed { 264 }

Ankit Vijay
May 31, 2014

x + y = 35 . . . ( i ) x y = 11 . . . ( i ) a d d i n g ( i ) a n d ( i i ) w e g e t 2 x = 48 x = 24 S u b s t i t u t i n g t h e v a l u e o f x w e g e t y = 11 H e n c e t h e a n s w e r i s 24 × 11 = 264 x+y=35\quad ...(i)\\ x-y=11\quad ...(i)\\ adding\quad (i)\quad and\quad (ii)\\ we\quad get\quad 2x=48\\ \quad \quad x=24\\ Substituting\quad the\quad value\quad of\quad x\quad we\quad get\\ \quad \quad y=11\\ Hence\quad the\quad answer\quad is\quad 24\times 11=264

difference is given here as 13 which means x-y=13 and we get x=24 and y=9 x*y=216 so I feel that ans should be none of these..pls clarify my statement...regards siva

siva shankar - 6 years, 11 months ago
Nemo Maximus
Jul 23, 2014

x + y = 35 x + y = 35 ...1

x y = 13 x - y = 13 ...2

Rearrange 1 to get

x = 35 y x = 35 -y

Substitute in 2

( 35 y ) y = 13 (35 - y) - y = 13

2 y = 13 35 -2 y = 13 - 35

y = 22 2 y = \frac{-22}{-2}

y = 11 y = 11

x = 35 y x = 35 - y

x = 35 11 x = 35 -11

x = 24 x = 24

x y = 264 xy = 264

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