Question

6. Розв'яжіть систему рiвнянь: a) [x-2y=3, [5x+y=4 методом пiдстановки; б) [2x+3y=5, [5x+2y=-4 методом додавання.​

Answer 1

a)

$\displaystyle\bf\\\left \{ {{x - 2y = 3} \atop {5x + y = 4 }} \right. \\ \displaystyle\bf\\\left \{ {{x = 2y + 3} \atop {5(2y +3 ) + y = 4}} \right. \\ \\ 10y +1 5 + y = 4 \\ 11y = 4 - 15 \\ 11y = - 11 \\ y = - 11 \div 11 \\ y = - 1 \\ \\ x = 2 \times ( - 1) + 3 \\ x = - 2 + 3 \\ x = 1$

Ответ: ( 1 ; - 1 )

б)

$\displaystyle\bf\\\left \{ {{2x + 3y = 5 \: \: | \times ( - 2)} \atop {5x + 2y = - 4 \: \: | \times 3 }} \right. \\ \displaystyle\bf\\ + \left \{ {{ - 4x - 6y = - 10} \atop {15x + 6y = - 12 }} \right. \\ \\ 15x - 4x = - 10 - 12 \\ 11x = - 22 \\ x = - 22 \div 11 \\ x = - 2 \\ \\ 2 \times ( - 2) + 3y = 5 \\ - 4 + 3y = 5 \\ 3y = 5 + 4 \\ 3y = 9 \\ y = 9 \div 3 \\ y = 3$

Ответ: ( - 2 ; 3 )