Question

8(х+у)+(х-у)=50, 12(х+у)+(х-у)=74

Answer 1

8(x+y)+(x-y)=50 12(x+y)+(x-y)=74

8x+8y+x-y=50 12x+12y+x-y=74

9x+7y=50 13x+11y=74

7y=50-9x 13x=74-11y

y=(50-9x)/7 x=(74-11y)/13

9x=50-7y 11y=74-13x

x=(50-7y)/9 y=(74-13x)/11

Answer 2

8(х+у)+(х-у)=50,

12(х+у)+(х-у)=74

умножим первое на минус 1 и сложим со вторым, получим

-8(х+у)-(х-у)=-50,

12(х+у)+(х-у)=74

4х+4у=24, х+у=6, откда у= 6-х подставим в первое уравнение, получим

8*6+х+х-6=50

2х=50-42

2х=8; х=4; у=6-4=2

Ответ (4;2)

Answer 3

To solve the given system of equations:

1. 8(x + y) + (x - y) = 50
2. 12(x + y) + (x - y) = 74

We can use the method of substitution or elimination to find the values of x and y. Let's use the elimination method:

Step 1: Multiply equation 1 by 3 and equation 2 by 2 to make the coefficients of (x - y) equal: 3 * [8(x + y) + (x - y)] = 3 * 50 => 24(x + y) + 3(x - y) = 150

2 * [12(x + y) + (x - y)] = 2 * 74 => 24(x + y) + 2(x - y) = 148

Step 2: Subtract equation 2 from equation 1: (24(x + y) + 3(x - y)) - (24(x + y) + 2(x - y)) = 150 - 148

Simplify: 24(x + y) + 3x - 3y - 24(x + y) - 2x + 2y = 2

Step 3: Combine like terms: 3x - 3y - 2x + 2y = 2

Step 4: Simplify: x - y = 2

Step 5: Now, let's find the values of x and y. We can use equation 1: 8(x + y) + (x - y) = 50

Substitute x - y = 2: 8(x + y) + 2 = 50

Step 6: Solve for x + y: 8(x + y) = 50 - 2 8(x + y) = 48 x + y = 48 / 8 x + y = 6

Step 7: Now, we have a system of two equations: x - y = 2 x + y = 6

Step 8: Add the two equations to eliminate y: (x - y) + (x + y) = 2 + 6

Simplify: 2x = 8

Step 9: Solve for x: x = 8 / 2 x = 4

Step 10: Substitute the value of x into one of the equations to find y. Let's use x + y = 6: 4 + y = 6

Step 11: Solve for y: y = 6 - 4 y = 2

The solution to the system of equations is x = 4 and y = 2.