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Oblicz układ równań metodą podstawiania zad. w załączniku



Oblicz Układ Równań Metodą Podstawiania Zad W Załączniku class=

Odpowiedź :

ZbiorJ

[tex]\left \{ {{6x-2y=5} \atop {3x+4y=15}} \right. \\\\\left \{ {{2y=6x-5} \atop {3x+2\cdot 2y=15}} \right. \\\\\left \{ {{2y=6x-5} \atop {3x+2\cdot (6x-5)=15}} \right. \\\\\left \{ {{2y=6x-5} \atop {3x+12x-10=15}} \right. \\\\\left \{ {{2y=6x-5} \atop {15x=15+10}} \right. \\\\\left \{ {{2y=6x-5} \atop {15x=25}~~\mid \div 15} \right. \\\\\left \{ {{x=\frac{5}{3} } \atop {2y=6x-5}} \right. \\\\\left \{ {{x=1\frac{2}{3} } \atop {2y=6\cdot \frac{5}{3} -5}} \right. \\\\[/tex]

[tex]\left \{ {{x=1\frac{2}{3} } \atop {2y=10-5}} \right. \\\\\left \{ {{x=1\frac{2}{3} } \atop {2y=5~~\mid \div 2}} \right. \\\\\left \{ {{x= 1\frac{2}{3}} \atop {y=\frac{5}{2} }} \right. \\\\\left \{ {{x= 1\frac{2}{3}} \atop {y=2\frac{1}{2} }} \right.[/tex]

LoczeeQ

[tex]6x - 2y = 5 \\ 3x + 4y = 15[/tex]

[tex]6x = 5 + 2y | \div 6 \\ x = \frac{5}{6} + \frac{1}{3} y[/tex]

[tex]3( \frac{5}{6} + \frac{1}{3} y) + 4y = 15 \\ \frac{15}{6} + y + 4y = 15 \\ \frac{5}{2} + 5y = 15 \\ 5y = 15 - \frac{5}{2} \\ 5y = \frac{30}{2} - \frac{5}{2} \\ 5y = \frac{25}{2} | \div 5 \\ y = \frac{25}{2} \times \frac{1}{5} = \frac{5}{2} [/tex]

[tex]x = \frac{5}{6} + \frac{1}{3} \times \frac{5}{2} \\ x = \frac{5}{6} + \frac{5}{6} \\ x = \frac{10}{6} = \frac{5}{3} [/tex]

Czyli

[tex](x.y) = ( \frac{5}{3} . \frac{5}{2} )[/tex]

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