Question

-2(2х+1)+2,5=3(у+2)-8х. 8-5(4-х)=6у-(5-х) решите систему уравнений​

Answer 1

$\left \{ {{-2(2x+1)+2,5=3(y+2)-8x} \atop {8-5(4-x)=6y-(5-x)}} \right. \\\\\left \{ {{-4x - 2 + 2,5 = 3y + 6 - 8x} \atop {8-20+5x = 6y - 5 +x}} \right.\\ \\\left \{ {{-4x + 8x - 3y = 6 + 2 - 2,5} \atop {5x - x - 6y = -5 - 8 +20}} \right.\\ \\\left \{ {{4x - 3y = 5,5} \atop {4x - 6y = 7}} \right.\\\\\left \{ {{4x - 3y = 5,5} \atop {-4x + 6y = -7}} \right. \\\\3y = -1,5\\y = - 0,5\\\\\left \{ {{4x - 3y = 5,5} \atop {y = -0,5}} \right. \\\\\left \{ {{4x - (-1,5) = 5,5} \atop {y = -0,5}} \right.$

$\left \{ {{4x+1,5 = 5,5} \atop {y = -0,5}} \right. \\\\\left \{ {{4x = 4} \atop {y = -0,5}} \right. \\\\\left \{ {{x = 1} \atop {y = -0,5}} \right.$

Ответ: (1; -0,5)

Answer 2

To solve the system of equations, we'll start by solving each equation separately and then find the values of 'x' and 'y' that satisfy both equations simultaneously.

1. -2(2x + 1) + 2.5 = 3(y + 2) - 8x

Let's simplify the equation step by step:

-4x - 2 + 2.5 = 3y + 6 - 8x

Next, combine like terms:

-4x + 0.5 = 3y - 8x + 6

Now, move all terms with 'x' to one side and all terms with 'y' to the other side:

-4x + 8x = 3y - 6 - 0.5

4x = 3y - 6.5

Now, let's move all terms with 'x' to one side and all constant terms to the other side:

4x - 3y = -6.5

2. 8 - 5(4 - x) = 6y - (5 - x)

Let's simplify the equation step by step:

8 - 20 + 5x = 6y - 5 + x

Next, combine like terms:

-12 + 5x = 6y + x - 5

Now, move all terms with 'x' to one side and all terms with 'y' to the other side:

5x - x = 6y - 5 + 12

4x = 6y + 7

Now, let's move all terms with 'x' to one side and all constant terms to the other side:

4x - 6y = 7

Now, we have the following system of equations:

1. 4x - 3y = -6.5
2. 4x - 6y = 7

To solve this system, we can use the method of elimination. We'll subtract equation 1 from equation 2 to eliminate 'x':

(4x - 6y) - (4x - 3y) = 7 - (-6.5)

Simplifying:

4x - 6y - 4x + 3y = 7 + 6.5

Combine like terms:

-3y = 13.5

Now, isolate 'y' by dividing both sides by -3:

y = -13.5 / 3

y = -4.5

Now that we have the value of 'y', we can find 'x' by substituting this value into either of the original equations. Let's use the first equation:

4x - 3y = -6.5

4x - 3(-4.5) = -6.5

4x + 13.5 = -6.5

Now, move constant term to the other side:

4x = -6.5 - 13.5

4x = -20

Finally, divide both sides by 4 to find 'x':

x = -20 / 4

x = -5

So, the solution to the system of equations is x = -5 and y = -4.5.