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CBSE Class 12-commerce Answered

find k if the equations 2x+3y-z=5, 3x-y+4z=2, x+7y-6z=k are consistent
Asked by bala160307 | 26 Apr, 2019, 01:53: PM
answered-by-expert Expert Answer
T h e space e q u a t i o n s space a r e
2 x plus 3 y minus z equals 5 space.... space left parenthesis i right parenthesis
3 x minus y plus 4 z equals 2 space.... space left parenthesis i i right parenthesis
x plus 7 y minus 6 z equals k space.... space left parenthesis i i i right parenthesis
S i n c e comma space 2 over 3 not equal to fraction numerator 3 over denominator negative 1 end fraction not equal to fraction numerator negative 1 over denominator 4 end fraction
S o space t h e space e q u a t i o n s space w i l l space h a v e space u n i q u e space s o l u t i o n
S o l v i n g space e q u a t i o n s space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis space s i m u l tan e o u s l y comma space w e space h a v e
x equals 1 minus z
S u b s t i t u t i n g space x space i n space e q u a t i o n space left parenthesis i right parenthesis comma space w e space g e t
y equals z plus 1
N o w comma space s u b s t i t u t i n g space t h e space v a l u e s space o f space x space a n d space y space i n space e q u a t i o n space left parenthesis i i i right parenthesis comma space w e space g e t
1 minus z plus 7 z plus 7 minus 6 z equals k
rightwards double arrow k equals 8
Answered by Renu Varma | 26 Apr, 2019, 05:34: PM
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