Question

Решить задачу с помощью системы уравнений. Масса 2 слитков олова и 5 слитков свинца составляет 33 кг, а масса 6 слитков олова и 2 слитков свинца равна 34 кг. Какова масса одного слитка олова и какова масса одного слитка свинца?​

Answer 1

Объяснение:

1 слиток олова = х кг

1 слиток свинца = у кг

2х + 5у = 33 | * -3

6х + 2у = 34

-6х - 15у = -99

6х + 2у = 34

-13у = -65

6х + 2у = 34

1)

-13у = -65

у = -65 : (-13)

у = 5

2)

6х + 2у = 34

6х + 2*5 = 34

6х + 10 = 34

6х = 34 - 10

6х = 24

х = 24 : 6

х = 4

1 слиток олова = (х) = 4 кг

1 слиток свинца = (у) = 5 кг

Answer 2

Problem Analysis

We are given the information that the total mass of 2 lead ingots and 5 tin ingots is 33 kg, and the total mass of 6 lead ingots and 2 tin ingots is 34 kg. We need to find the mass of one lead ingot and the mass of one tin ingot.

Let's assume the mass of one lead ingot is L kg and the mass of one tin ingot is T kg. We can set up a system of equations based on the given information.

System of Equations

We can set up the following system of equations:

Equation 1: 2L + 5T = 33 Equation 2: 6L + 2T = 34

We can solve this system of equations to find the values of L and T.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.

Multiplying Equation 1 by 3 and Equation 2 by 5, we get:

Equation 3: 6L + 15T = 99 Equation 4: 30L + 10T = 170

Subtracting Equation 4 from Equation 3, we get:

(6L + 15T) - (30L + 10T) = 99 - 170 -24L + 5T = -71

Now, we have a new equation:

Equation 5: -24L + 5T = -71

We can solve Equation 5 for T:

5T = -71 + 24L T = (-71 + 24L) / 5

Substituting this value of T into Equation 1, we get:

2L + 5((-71 + 24L) / 5) = 33 2L - 71 + 24L = 165 26L - 71 = 165 26L = 236 L = 236 / 26 L = 9.08

Now that we have the value of L, we can substitute it back into Equation 1 to find T:

2(9.08) + 5T = 33 18.16 + 5T = 33 5T = 33 - 18.16 5T = 14.84 T = 14.84 / 5 T = 2.968

Answer

The mass of one lead ingot is approximately 9.08 kg and the mass of one tin ingot is approximately 2.968 kg.

Please note that the values are approximate due to rounding.

Let me know if you need any further assistance!