Question

21(x-y)=48+20x19(y+x)=100+12y​

Answer 1

1) 21(х-у)=48+20х

21х-21у=48+20х

21х-20х=48+21у

итак, первое уравнение привели к виду х=48+21у

2)подставим его во   второе уравнение

19(у+48+21у)=100+12у

упростим это уравнение.

19*48+19*22у=100+12у

418у-12у=100-912

403у=-812

406у=-812

у=-2    х= 48-2*21 тогда х= 48- 42; х=6

Ответ(6; -2)

Answer 2

To solve the system of equations:

1. 21(x - y) = 48 + 20x
2. 19(y + x) = 100 + 12y

Let's start by simplifying the equations:

1. Distribute the 21 on the left side of the first equation: 21x - 21y = 48 + 20x

2. Distribute the 19 on the left side of the second equation: 19y + 19x = 100 + 12y

Now, let's isolate one of the variables in each equation:

1. For equation (1): Move all the terms with x to one side by subtracting 20x from both sides: 21x - 20x - 21y = 48 x - 21y = 48

2. For equation (2): Move all the terms with y to one side by subtracting 19y from both sides: 19x - 19y - 12y = 100 19x - 31y = 100

Now we have a system of two equations:

1. x - 21y = 48
2. 19x - 31y = 100

We can use substitution or elimination to solve this system. Let's use the elimination method:

Step 1: Multiply both sides of equation (1) by 19 to make the coefficients of x in both equations the same: 19(x - 21y) = 19(48) 19x - 399y = 912

Step 2: Now we have two equations with the same coefficient for x: 19x - 399y = 912 (Equation 1 after multiplication) 19x - 31y = 100 (Equation 2)

Step 3: Subtract equation (2) from equation (1) to eliminate x: (19x - 399y) - (19x - 31y) = 912 - 100 19x - 399y - 19x + 31y = 812 -368y = 812

Step 4: Solve for y: y = 812 / -368 y ≈ -2.2 (approximately)

Step 5: Substitute the value of y back into equation (1) to find x: x - 21(-2.2) = 48 x + 46.2 = 48 x ≈ 1.8 (approximately)

So, the solution to the system of equations is approximately x ≈ 1.8 and y ≈ -2.2.