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Elimination Method of Finding Solution of a Pair of Linear Equations

One number is...

Question

One number is four less than three times another. if their sum is increased by 5 the answer is 25. Find the number.

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Solution

Dear Student,

Let numbers are x and y.

$G i v e n t h a t o n e n u m b e r i s 4 l e s s t h a n 3 t i m e s t h e a n o t h e r x = 3 y - 4 - - (1) n o w i f s u m i s i n r e a s e d b y 5 t h e r e s u l t i s 25 x + y + 5 = 25 x + y = 20 - - (2) s o l v i n g t w o e q u a t i o n s p u t x = 3 y - 4 i n e q u a t i o n 2 3 y - 4 + y = 20 4 y - 4 = 20 4 y = 24 y = \frac{24}{4} y = 6 P u t y = 6 i n e q u a t i o n x + y = 20 x + 6 = 20 x = 20 - 6 x = 14 H e n c e x = 14 a n d y = 6$

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