a)
[tex]2x + 6y = 4 \\ 5x - 2y = - 24[/tex]
[tex]2x = 4 - 6y | \div 2 \\ x = 2 - 3y[/tex]
[tex]5(2 - 3y) - 2y = - 24 \\ 10 - 15y - 2y = - 24 \\ - 17y = - 34 | \div ( - 17) \\ y = 2[/tex]
[tex]2x = 4 - 6 \times 2 \\ 2x = 4 - 12 \\ 2x = - 8 | \div 2 \\ x = - 4[/tex]
Sprawdzenie
[tex]2( - 4) + 6 \times 2 = 4 \\ - 8 + 12 = 4[/tex]
[tex]5( - 4) - 2 \times 2 = - 24 \\ - 20 - 4 = - 24[/tex]
Zgadza się
[tex]x = - 4 \\ y = 2[/tex]
b)
[tex]5x - 4y = - 12 \\ 3x - 8y = - 3[/tex]
[tex]5x - 4y = - 12 \\ 5x = - 12 + 4y | \div 5 \\ x = - \frac{12}{5} + \frac{4}{5} y[/tex]
[tex]3( - \frac{12}{5} + \frac{4}{5} y) - 8y = - 3 \\ - \frac{36}{5} + \frac{12}{5} y - 8y = - 3 \\ - \frac{36}{5} - \frac{28}{5} y = - 3 | \times 5 \\ - 36 - 28y = - 15 \\ - 28y = - 15 + 36 \\ - 28y = 21 | \div ( - 28) \\ y = - \frac{21}{28} = - \frac{3}{4} [/tex]
[tex]x = - \frac{12}{5} + \frac{4}{5} ( - \frac{3}{4} ) \\ x = - \frac{12}{5} - \frac{3}{5} \\ x = - \frac{15}{5} \\ x = - 3[/tex]
Sprawdzenie
[tex]5( - 3) - 4( - \frac{3}{4} ) = - 12 \\ - 15 + 3 = - 12[/tex]
Zgadza się
[tex]3( - 3) - 8( - \frac{3}{4} ) = - 3 \\ - 9 + 6 = - 3[/tex]
Zgadza się
[tex]x = - 3 \\ y = - \frac{3}{4} [/tex]
