Question

Розв'яжіть систему рівнянь способом додавання: 1) { 7x+y= 2, 5x-4y=25 2) 2x+3y =- 1; x-y=3​

Answer 1

1)

$\displaystyle\bf\\\left \{ {{7x + y = 2 \: \: | \times 4} \atop {5x - 4y = 25 }} \right. \\ \displaystyle\bf\\ + \left \{ {{28x + 4y = 8} \atop {5x - 4y = 25 }} \right. \\ \\ 5x + 28x = 8 + 25 \\ 33x = 33 \\ x = 33 \div 33 \\ x = 1 \\ \\ 7 \times 1 + y = 2 \\ y = 2 - 7 \\ y = - 5$

Ответ: ( 1 ; - 5 )

2)

$\displaystyle\bf\\\left \{ {{2x + 3y = - 1} \atop {x - y = 3 \: \: | \times 3 }} \right. \\ \displaystyle\bf\\ + \left \{ {{2x + 3y = - 1} \atop {3x - 3y = 9 }} \right. \\ \\ 2x + 3x = 9 - 1 \\ 5x = 8 \\ x = 8 \div 5 \\ x = 1.6 \\ \\ 1.6 - y = 3 \\ y = 1.6 - 3 \\ y = - 1.4$

Ответ: ( 1,6 ; - 1,4 )