Question

7*. Розв’язати систему рівнянь:

Answer 1

$\displaystyle\bf\\\left \{ {{ \frac{x + 3}{2} - \frac{y - 2}{3} = 2 \: \: | \times 6 } \atop { \frac{x - 1}{4} + \frac{y + 1}{3} = 4 \: \: | \times 12}} \right. \\ \displaystyle\bf\\\left \{ {{3(x + 3) - 2(y - 2) = 12} \atop {3(x - 1) + 4(y + 1) = 48 }} \right. \\ \displaystyle\bf\\\left \{ {{3x + 9 - 2y + 4 = 12} \atop {3x - 3 + 4y + 4 = 48 }} \right. \\ \displaystyle\bf\\\left \{ {{3x - 2y = - 1 \: \: | \times ( - 1)} \atop {3x + 4y = 47 }} \right. \\ \displaystyle\bf\\ + \left \{ {{ - 3x + 2y = 1} \atop {3x + 4y = 47 }} \right. \\ \\ 2y + 4y = 1 + 47 \\ 6y = 48 \\ y = 48 \div 6 \\ y = 8 \\ \\ 3x - 2 \times 8 = - 1 \\ 3x - 16 = - 1 \\ 3x = - 1 + 16 \\ 3x = 15 \\ x = 15 \div 3 \\ x = 5$

Ответ: ( 5 ; 8 )