Question

Решите методом подстановки систему уравнений

Answer 1

Объяснение:

1)

$\left \{ \begin{array}{lcl} {{x+2y=4,} \\ {3x-4y=2;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{x=4-2y,} \\ {3(4-2y)-4y=2}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{x=4-2y,} \\ {12-6y -4y=2;}} \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{x=4-2y,} \\ {-10y=-10;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{x=4-2*1,} \\ {y=1;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{x=2,} \\ {y=1.}} \end{array} \right.$

ответ: ( 2; 1 )

2)

$\left \{ \begin{array}{lcl} {3x+{y=4,} \\ {5x-2y=14;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{y=4-3x,} \\ {5x-2(4-3x)=14;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{y=4-3x,} \\ {5x-8+6x=14;}} \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{y=4-3x,} \\ {11x=22;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{y=4-3*2,} \\ {x=2;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{y=-2,} \\ {x=2.}} \end{array} \right.$

ответ: ( 2; -2 )

3)

$\left \{ \begin{array}{lcl} {2x+7{y=11,} \\ {4x-y=7;}} \end{array} \right.\Leftrightarrow \left \{ \begin{array}{lcl} {{2x+7(4x-7)=11,} \\ {y=4x-7;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{2x+28x-49=11,} \\ {y=4x-7;}} \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{30x=60,} \\ {y=4x-7;}} \end{array} \right.\Leftrightarrow \left \{ \begin{array}{lcl} {{x=2,} \\ {y=4*2-7;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{x=2,} \\ {y=1.}} \end{array} \right.$

ответ: ( 2; 1 )

4)

$\left \{ \begin{array}{lcl} {{7x-4y=2,} \\ {5x+11y=43;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{7x-4y=2} \\ {5x=43-11y;}} \end{array} \Leftrightarrow\right.\left \{ \begin{array}{lcl} {{7( 8,6-2,2y)-4y=2,} \\ {x=8,6-2,2y;}} \end{array} \right.$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{60,2-15,4y-4y=2,} \\ {x=8,6-2,2y;}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{-19,4y=-58,2} \\ {x=8,6-2,2y}} \end{array} \right.\Leftrightarrow\left \{ \begin{array}{lcl} {{y=3,} \\ {x=8,6-2,2*3;}} \end{array} \right.$

$\Leftrightarrow\left \{ \begin{array}{lcl} {{y=3,} \\ {x=2.}} \end{array} \right.$

ответ: ( 2; 3 )