Question

Show that system of equation x-y=3 and 2x+3y=7 has unique solution

Answer 1

Answer:

it's problem of rank and non homogeneous systems of linear equations.

Answer 2

$Given \: system \:of \: linear \: equations : \\x -y - 3 = 0 \: and \: 2x+3y -7 = 0$

$Compare \:above \: equations \:with \\a_{1}x+b_{1}y+c_{1} = 0 \:and \:a_{2}x+b_{2}y+c_{2} = 0,\\we \: get$

$a_{1} = 1 , \: b_{1} = -1 , \:c_{1} = -3 \\and \: a_{2} = 2 , \: b_{2} = 3 , \:c_{2} = -7$

$\frac{a_{1}}{a_{2}} = \frac{1}{2} \: --(1)$

$and \:\frac{b_{1}}{b_{2}} = \frac{-1}{3} \: --(2)$

/* From (1) and (2) */

$\implies \blue{\frac{a_{1}}{a_{2}}}\pink { \neq }\blue{ \frac{b_{1}}{b_{2}}}$

Therefore.,

$\green { Given \: system \:of \: equations }\\\green { \:has \: unique \: solution }$

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