Question

Алгебра,Решить 3 системы рівнянь зручним способом.На листочке написать с { и по шагово пожалуйста.

Answer 1

1)

$\displaystyle\bf\\\left \{ {{2x - y = 3} \atop {3x - 2y = - 8 }} \right. \\ \displaystyle\bf\\\left \{ {{y = 2x - 3} \atop {3x - 2(2x - 3) = - 8}} \right. \\ \\ 3x - 4x + 6 = - 8 \\ - x = - 8 - 6 \\ - x = - 14 \\ x = 14 \\ \\ y = 2 \times 14 - 3 = 28 - 3 = 25$

Ответ: ( 14 ; 25 )

2)

$\displaystyle\bf\\\left \{ {{3x + y = 4 \: \: | \times 2 } \atop {7x - 2y = 5 }} \right. \\ \displaystyle\bf\\ + \left \{ {{6x + 2y = 8} \atop {7x - 2y = 5 }} \right. \\ \\ 6x + 7x = 8 + 5 \\ 13x = 13 \\ x =13 \div 13 \\ x = 1 \\ \\ 3 \times 1 + y = 4 \\ 3 + y = 4 \\ y = 4 - 3 \\ y = 1$

Ответ: ( 1 ; 1 )

3)

$\displaystyle\bf\\\left \{ {{ \frac{x}{3} + \frac{y}{4} - 2 = 0 \: \: | \times 12 } \atop {2x - y = 2 }} \right. \\ \displaystyle\bf\\\left \{ {{4x + 3y = 24} \atop {2x - y = 2 \: \: | \times 3}} \right. \\ \displaystyle\bf\\ + \left \{ {{4x + 3y = 24} \atop {6x - 3y = 6 }} \right. \\ \\ 4x + 6x = 2 4+ 6 \\ 10x = 30 \\ x = 30 \div 10 \\ x = 3 \\ \\ 2 \times 3 - y = 2 \\ 6 - y = 2 \\ y = 6 - 2 \\ y = 4$

Ответ: ( 3 ; 4 )