Question

Решите систему уравнений спсобом подстановки:5х-3у=1х+2у=5Прошу написать и решение и ответ

Answer 1

5х-3у=1        х=5-2у               

х+2у=5         5(5-2у)-3у=1

 

25-10у-3у=1

13у=24

у=24/13 = 1 11/13              х=5 - 2 * 24/13

                                         х=17/13 = 1 4/13

Ответ: х= 1 4/13;   у=1 11/13                                                                        

                                                                 

 

Answer 2

5х-3у=1 х=5-2y

х+2у=5 5(5-2у)-3у=1

25-10у-3у=1
13у=24

у=24/13 = 1 11/13 х=5 - 2 * 24/13
х=17/13 = 1 4/13

Ответ: х= 1 4/13; у=1 11/13 

Answer 3

To solve the system of equations using the method of substitution, we will solve one equation for one variable and substitute it into the other equation. Let's solve the given system of equations step by step:

Step 1: Solve the first equation for x

The first equation is 5x - 3y = 1. We can isolate x by adding 3y to both sides of the equation: 5x - 3y + 3y = 1 + 3y 5x = 3y + 1 Dividing both sides by 5, we get: x = (3y + 1)/5

Step 2: Substitute the value of x into the second equation

The second equation is x + 2y = 5. We will substitute the value of x from Step 1 into this equation: (3y + 1)/5 + 2y = 5 Multiplying both sides by 5 to eliminate the denominator, we get: 3y + 1 + 10y = 25 Combining like terms, we have: 13y + 1 = 25 Subtracting 1 from both sides, we get: 13y = 24 Dividing both sides by 13, we get: y = 24/13

Step 3: Find the value of x

Now that we have the value of y, we can substitute it back into the equation we found in Step 1 to find the value of x: x = (3(24/13) + 1)/5 Simplifying, we get: x = (72/13 + 1)/5 x = (72/13 + 13/13)/5 x = 85/13 / 5 x = 85/65 x = 17/13

Solution:

The solution to the given system of equations is x = 17/13 and y = 24/13.

Please note that the solution has been calculated using the method of substitution.