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Maths-

General

Easy

Question

$T h e space s$ olution o $f space 2 x plus y plus Z equals 1 comma x minus 2 y minus 3 z equals 1 comma$ $3 x plus 2 y plus 4 z equals 5$ is

1,2,3
1,2,‐3
1,‐3,2
1,3,2

hint Hint:

Use combination of elimination and substitution method to obtain the answer.

The correct answer is: 1,‐3,2

$2 x plus y plus z equals 1 space space space space space...... open parentheses 1 close parentheses x minus 2 y minus 3 z equals 1 space space space space..... open parentheses 2 close parentheses 3 x plus 2 y plus 4 z equals 5 space space space...... open parentheses 3 close parentheses M u l t i p l y space e q u a t i o n space open parentheses 1 close parentheses space b y space open parentheses 4 close parentheses comma 8 x plus 4 y plus 4 z equals 4 S u b t r a c t i n g space a b o v e space e q u a t i o n space w i t h space e q u a t i o n space open parentheses 3 close parentheses comma 8 x plus 4 y plus 4 z equals 4 3 x plus 2 y plus 4 z equals 5 minus space space minus space space space space minus space space space space space minus minus negative negative negative negative negative negative negative 5 x plus 2 y equals negative 1 2 y equals open parentheses negative 1 minus 5 x close parentheses y equals fraction numerator negative 1 minus 5 x over denominator 2 end fraction space space space space space..... open parentheses 4 close parentheses S u b t r a c t i n g space e q u a t i o n space open parentheses 3 close parentheses space f r o m space open parentheses 2 close parentheses comma x minus 2 y minus 3 z equals 1 3 x plus 2 y plus 4 z equals 5 minus negative negative negative negative negative negative negative 4 x plus z equals 6 z equals 6 minus 4 x space space space space space space....... open parentheses 5 close parentheses P u t t i n g space e q u a t i o n space open parentheses 4 close parentheses space a n d space open parentheses 5 close parentheses space i n space e q u a t i o n space open parentheses 2 close parentheses comma x minus 2 y minus 3 z equals 1 x minus 2 open parentheses fraction numerator negative 1 minus 5 x over denominator 2 end fraction close parentheses minus 3 open parentheses 6 minus 4 x close parentheses equals 1 x plus 1 plus 5 x minus 18 plus 12 x equals 1 18 x equals 18 therefore x equals 1 P u t t i n g space v a l u e space o f space x space i n space e q u a t i o n space 4 space a n d space 5 comma y equals negative 1 minus 5 x equals negative 1 minus 51 equals negative 6 equals negative 3 z equals 6 minus 4 x equals 6 minus 41 equals 6 minus 4 equals 2 H e n c e comma space w e space g e t x equals 1 y equals negative 3 z equals 2$

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