Question

Решить систему уравнений. 5(3x+y) - 8(x-6y) = 20 6(x-10y) - 13(x-y) = 52.

Answer 1

 15x+5y-8x+48y=20
6x-60y-13x+13y=52

7x+53y=20
-7x-47y=52

Складываем

6y=72
y=72:6
y=12

7x+53*12=20
7x=20-636
7x=-616
x=-616:7
x=-88

Answer 2

5(3x+y)-8(x-6y)=20
15x+5y-8x+48y=20
7x+53y=20
7x=20-53y
x=20/7-53/7y
==================
7x+53*12=20
7x+636=20
7x=20-636
7x=-616
x=-88

Answer 3

To solve the system of equations:

1. 5(3x + y) - 8(x - 6y) = 20
2. 6(x - 10y) - 13(x - y) = 52

We will first simplify both equations and then use either the substitution or elimination method to find the values of x and y.

Let's simplify the equations step by step:

1. Distribute the terms:

   15x + 5y - 8x + 48y = 20

2. Combine like terms:

   (15x - 8x) + (5y + 48y) = 20

   7x + 53y = 20

Now, let's simplify the second equation:

1. Distribute the terms:

   6x - 60y - 13x + 13y = 52

2. Combine like terms:

   (6x - 13x) + (-60y + 13y) = 52

   -7x - 47y = 52

Now we have the simplified system of equations:

1. 7x + 53y = 20
2. -7x - 47y = 52

Now, we can use the elimination method to solve the system. We want to eliminate one variable by adding or subtracting the equations. Let's add the two equations:

(7x + 53y) + (-7x - 47y) = 20 + 52

Simplifying:

6y = 72

Now, divide both sides by 6 to solve for y:

y = 12

Now that we have the value of y, we can substitute it back into either of the original equations to find the value of x. Let's use the first equation:

7x + 53(12) = 20

7x + 636 = 20

Now, isolate x:

7x = 20 - 636

7x = -616

Finally, divide both sides by 7 to solve for x:

x = -616 / 7

x ≈ -88

So, the solution to the system of equations is approximately:

x ≈ -88 y = 12