Question

23(x – y) = 17 + 2x,2(y – x) = 13 – x.​

Answer 1

Ответ:

(-73; -30)

Пошаговое объяснение:

Система уравнений:

3(x-y)=17+2x; 3x-3y=17+2x; x-3y=17

2(y-x)=13-x; 2y-2x=13-x; 2y-x=13

x-3y+2y-x=17+13

-y=30

y=-30

2·(-30)-x=13

x=-60-13=-73

Answer 2

To solve this system of equations:

1. First, we can simplify the equations:

   Equation 1: 23(x - y) = 17 + 2x Equation 2: 2(y - x) = 13 - x

2. Expand and distribute on both sides of the equations:

   Equation 1: 23x - 23y = 17 + 2x Equation 2: 2y - 2x = 13 - x

3. Rearrange the terms in both equations to isolate the x and y terms on one side:

   Equation 1: 23x - 2x = 23y + 17 Equation 2: 2y + x = 13

4. Simplify the equations:

   Equation 1: 21x = 23y + 17 Equation 2: x + 2y = 13

5. Now you have a system of two equations with two variables:

   21x = 23y + 17 x + 2y = 13

6. You can solve this system of equations using various methods, such as substitution or elimination. I'll use the elimination method here.

   Multiply the second equation by 21 to make the coefficients of x in both equations equal:

   21(x + 2y) = 21(13)

   This results in:

   21x + 42y = 273

7. Now, you can subtract the first equation from the new equation to eliminate x:

   (21x + 42y) - (21x = 23y + 17)

   This simplifies to:

   42y - 23y = 273 - 17

   19y = 256

8. Solve for y by dividing both sides by 19:

   y = 256 / 19

9. Now that you have the value of y, you can substitute it back into one of the original equations to find the value of x. Let's use the second equation:

   x + 2(256 / 19) = 13

10. Solve for x:

x + (512 / 19) = 13

x = 13 - (512 / 19)

To get a simplified fraction for x, you can find a common denominator for 13:

x = (19/19 * 13) - (512 / 19)

x = (247 - 512) / 19

x = -265 / 19

So, the solution to the system of equations is:

x = -265/19 y = 256/19