Question

4. Розв'яжіть систему рівнянь

Answer 1

1)

$\displaystyle\bf\\\left \{ {{2x + 9y = 2 \: \: | \times ( - 4)} \atop {8x - 15y = 25 }} \right. \\ \displaystyle\bf\\ + \left \{ {{ - 8x - 36y = - 8} \atop {8x - 15y = 25 }} \right. \\ \\ - 36y - 15y = 25 - 8 \\ - 51y = 17 \\ y = 17 \div ( - 51) \\ y = - \frac{1}{3} \\ \\ 2x + 9 \times ( - \frac{1}{3} ) = 2 \\ 2x - 3 = 2 \\ 2x = 2 + 3 \\ 2x = 5 \\ x = 5 \div 2 \\ x = 2.5$

ответ: ( 2,5 ; - 1/3 )

2)

$\displaystyle\bf\\\left \{ {{ \frac{3x - 2y}{3} - \frac{4x + 5}{4} = \frac{7x - 10}{8} \: \: | \times 24 } \atop { \frac{6x - 5y}{2} + \frac{2x + y}{5} = x + 2y \: \: | \times 10}} \right. \\ \displaystyle\bf\\\left \{ {{8(3x - 2y) - 6(4x + 5) = 3(7x - 10)} \atop {5(6x - 5y) + 2(2x + y) = 10(x + 2y) }} \right. \\ \displaystyle\bf\\\left \{ {{24x - 16y - 24x - 30 = 21x - 30} \atop {30x - 25y + 4x + 2y = 10x + 20y }} \right. \\\displaystyle\bf\\\left \{ {{ - 21x - 16y = 0 \: \: | \times 8} \atop {24x - 43y = 0 \: \: | \times 7 }} \right. \\ \\ \displaystyle\bf\\ + \left \{ {{ - 168x - 128y = 0} \atop {168x - 301y = 0 }} \right. \\ \\ - 128y - 301y = 0 \\ - 429y = 0 \\ y = 0 \\ \\ - 21x - 16 \times 0 = 0 \\ - 21x = 0 \\ x = 0$

ответ: ( 0 ; 0 )