Question

-2х+3y=11 x+2y=3 решить систему способом сложения

Answer 1

Ответ:

Объяснение:

2е уравнение умножим на 2

получим 2x+4y=6

теперь сложим 2 уравнения

-2x+3y=11

+

2x+4y=6

=

-2x+2x+3y+4y=17   =>7y=17; y=17/7

подставим y во второе уравнение

x+2(17/7)=3

x=3-(34/7)

x=-13/7

y=$2\frac{3}{7}$

$x=-1\frac{6}{7}$

Answer 2

To solve this system of equations by the method of addition, we need to add the two equations together in a way that eliminates one of the variables. We can do this by multiplying the second equation by -2 and then adding it to the first equation:

-2(x + 2y) + 3y = -6 - 2y + 3y -2x - 4y + 3y = -2 -2x - y = -2

Now we have a new equation with only one variable, -x, and its coefficient is not equal to 1. We can solve for x by isolating the variable:

-2x - y = -2 -2x = y - 2 x = (y - 2) / (-2)

Now we can substitute this expression for x into one of the original equations, say the second equation, to solve for y:

x + 2y = 3 [(y - 2) / (-2)] + 2y = 3 y - 4y + 4 = -6 -3y = -10 y = 10 / 3

Finally, we can substitute this value of y back into either equation to solve for x:

-2x + 3y = 11 -2x + 3(10/3) = 11 -2x + 10 = 11 -2x = 1 x = -1/2

Therefore, the solution to the system of equations is x = -1/2 and y = 10/3.