Ответ:
5 + 2(х - 1) = 5 + 2х + (-2) = 3 + 2х
Для начала раскрываем скобки: при умножении 2 на -1 получаем -2, т.к. умножаем положительное на отрицательное. А затем складываем 5 и -2, получается, соответственно, 3
В 9 задании:
так функции убывающие, то к₁ и к₂ должно быть меньше 1 (отрицательным)
Если пересекаются во второй четверти, то х - отрицательный, а у - положительный
Исходя из формулы подбираем числа
<span>Дана система ур-ний</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Из 1-го ур-ния выразим x</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span>Перенесем слагаемое с переменной y из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span>Разделим обе части ур-ния на множитель при x</span>
<span /><span><span><span><span><span><span><span><span><span><span>3</span><span>x</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>1</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>(</span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span>)</span></span></span><span /></span></span><span /></span><span>3x3=13(−y+2)</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>Подставим найденное x в 2-е ур-ние</span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Получим:</span>
<span /><span><span><span><span><span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span><span><span>(</span></span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>)</span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−y+2(−y3+23)=3</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>4</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−5y3+43=3</span></span>
<span>Перенесем свободное слагаемое 4/3 из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span>Разделим обе части ур-ния на множитель при y</span>
<span /><span><span><span><span><span><span><span><span><span><span>−</span><span>1</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>y<span /></span></span><span /></span><span><span><span>−</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span><span><span /><span /></span></span></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>−153y−53=−1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>y=−1</span></span>
<span>Т.к.</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>то</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span><span>−</span><span>1</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−−13+23</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span>Ответ:</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span></span><span>
</span>
Пусть х человек работает во втором цехе. тогда в первом - 2х
в третьем 2х+20
всего 970
2х+х+2х+20=970
5х=970-20
5х=950
х=950÷5
х=190 человек во втором цехе
1) 190×2=380 человек в первом цехе
2)380+20=400 человек в третьем
ответ : 380, 190, 400