решите систему уравнений способом подстановки. Created by ainurlove19. matematika-ru

1){ (2x+1)/3 - (x-2y)/5 = 4(2x+y)/15 |*15{ (x-4y)/3 + (5x-11y)/6 = (3x-1)/4 |*12{ 5(2x+1) - 3(x-2y) = 4(2x+y){4(x-4y) + 2(5x-11y) = 3(3x-1){10x+5 - 3x +6y = 8x+4y{4x-16y +10x-22y = 9x-3{7x + 6y + 5 = 8x +4y{14x - 38y = 9x- 3{7x + 6y - 8x - 4y = - 5{14x - 38y - 9x = -3{-x + 2y = - 5 ⇒ x = 2y+5{ 5x - 38y = -35(2y + 5) -38y = -310y + 25 -38y = -3-28y = - 3 - 25-28y = -28y = 1x= 2*1 + 5x=7ответ: (7; 1)2) {(7х +у) / 3 - (5х-у)/2 = (х+у) / 6 | *6{ (9x-2y)/8 + (7x+4y)/6 = (x+y)/3 + 4 |*24{2(7x+y) - 3(5x-y) = x+y{3(9x-2y) + 4(7x+4y) = 8(x+y) + 4*24{14x +2y -15x +3y = x+y{ 27x -6y +28x +16y = 8x+8y +96{-x + 5y = x+y{55x +10y = 8x+8y +96{ 5y -y = x+x{ 55x +10y -8x - 8y =96{ 4y = 2x ⇒ y = 2x/4 ⇒ y = 1/2 * x ⇒ y = 0.5x{ 47x +2y =9647x + 2 *0.5x = 9647x + x=9648x = 96x= 96 :48х= 2у= 0,5*2у=1ответ : (2 ; 1)Новые вопросы в МатематикаПомогите пожалуйста завтра екзамен СРОЧНО ДАЮ 40 БАЛЛОВУ математичному таборі займатися 96 учнів 8-го, 9-го і 10-гокласу. Учні 8 кл склали 0,8 кількості учнів 9-го класу, а 10-го кла…сусклало 33 1/3% сумарного числа 8-го та 9-го класів. Скільки учнівкожного класу займаються у математичному таборі?СРОЧНО ПОМОГИТЕ 500×пи Допоможіть будь ласка, з поясненням 36. Туристы прошли весь маршрут за 3 дня. В первый день они прошли треть пути, а во второй 4/9 всего пути, а в третий оставшиеся 24км. Какова длина вс…его маршрута? СРОЧНО!!У класi число відсутніх учнів складае частину від числа 1/6 присутніх. Коли з класу ви- йшов 1 учень, число відсутніх склало 20% від числа при…сут- ніх. Скільки всього учнів у класi?Длинна 125 м какая ширина и длинна ипериметр площадь 1 haПомогите срочно пожалуйста 5,6Помогите пожалуйста, очень срочно нужно!Помогите 5,6ПожалуйстаПредыдущийСледующийВместе мы знаем большеЭтот сайт использует cookies Политика Cookies . 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решите систему уравнений способом подстановки...

ainurlove19 @ainurlove19

July 2022 1 1 Report

решите систему уравнений способом подстановки

Answers & Comments

zhenyaM2002

Verified answer

1)
{ (2x+1)/3 - (x-2y)/5 = 4(2x+y)/15 |*15
{ (x-4y)/3 + (5x-11y)/6 = (3x-1)/4 |*12

{ 5(2x+1) - 3(x-2y) = 4(2x+y)
{4(x-4y) + 2(5x-11y) = 3(3x-1)

{10x+5 - 3x +6y = 8x+4y
{4x-16y +10x-22y = 9x-3

{7x + 6y + 5 = 8x +4y
{14x - 38y = 9x- 3

{7x + 6y - 8x - 4y = - 5
{14x - 38y - 9x = -3

{-x + 2y = - 5 ⇒ x = 2y+5
{ 5x - 38y = -3
5(2y + 5) -38y = -3
10y + 25 -38y = -3
-28y = - 3 - 25
-28y = -28
y = 1

x= 2*1 + 5
x=7

ответ: (7; 1)

2)
{(7х +у) / 3 - (5х-у)/2 = (х+у) / 6 | *6
{ (9x-2y)/8 + (7x+4y)/6 = (x+y)/3 + 4 |*24

{2(7x+y) - 3(5x-y) = x+y
{3(9x-2y) + 4(7x+4y) = 8(x+y) + 4*24

{14x +2y -15x +3y = x+y
{ 27x -6y +28x +16y = 8x+8y +96

{-x + 5y = x+y
{55x +10y = 8x+8y +96

{ 5y -y = x+x
{ 55x +10y -8x - 8y =96

{ 4y = 2x ⇒ y = 2x/4 ⇒ y = 1/2 * x ⇒ y = 0.5x
{ 47x +2y =96
47x + 2 *0.5x = 96
47x + x=96
48x = 96
x= 96 :48
х= 2

у= 0,5*2
у=1
ответ : (2 ; 1)