show that 2 X + 3 y = 7 and 6x-y=2has unique solution
Answers
Answer:
show that 2 X + 3 y = 7 and 6x-y=2has unique solution
Step-by-step explanation:
Givensystemoflinearequations:
x−y−3=0and2x+3y−7=0
\begin{gathered} Compare \:above \: equations \:with \\a_{1}x+b_{1}y+c_{1} = 0 \:and \:a_{2}x+b_{2}y+c_{2} = 0,\\we \: get \end{gathered}
Compareaboveequationswith
a
1
x+b
1
y+c
1
=0anda
2
x+b
2
y+c
2
=0,
weget
\begin{gathered} a_{1} = 1 , \: b_{1} = -1 , \:c_{1} = -3 \\and \: a_{2} = 2 , \: b_{2} = 3 , \:c_{2} = -7 \end{gathered}
a
1
=1,b
1
=−1,c
1
=−3
anda
2
=2,b
2
=3,c
2
=−7
\frac{a_{1}}{a_{2}} = \frac{1}{2} \: --(1)
a
2
a
1
=
2
1
−−(1)
and \:\frac{b_{1}}{b_{2}} = \frac{-1}{3} \: --(2)and
b
2
b
1
=
3
−1
−−(2)
/* From (1) and (2) */
\implies \blue{\frac{a_{1}}{a_{2}}}\pink { \neq }\blue{ \frac{b_{1}}{b_{2}}}⟹
a
2
a
1
=
b
2
b
1
Therefore.,
\begin{gathered} \green { Given \: system \:of \: equations }\\\green { \:has \: unique \: solution } \end{gathered}
Givensystemofequations
hasuniquesolution
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