Question

Решите систему уравнений 5x-3y=0 3x-4y=29 и вот ещё 2x+y=12 7x-2y=31 Заранее спасибо)))

Answer 1

1.
5x-3y=0
3x-4y=29

Умножим первое уравнение на (-3), второе на 5
-15х+9у=0
15х-20у=145

Складываем
-11у=145
у=-145/11=-13 целых 2/11

х=(29+4у)/3= (29+4·(-145/11))/3=(29·11-4·145)/33=-261/33=-87/11=-7целых 10/11
Ответ. (-7целых 10/11; -13 целых 2/11)
2.
2x+y=12
7x-2y=31
Умножаем первое уравнение на 2
4x+2y=24
7x-2y=31
Складываем
11х=55
х=5
у=12-2х=12-2*5=2
Ответ. (5;2)

Answer 2

Solving the System of Equations

To solve the system of equations:

1. 5x - 3y = 0 2. 3x - 4y = 29 3. 2x + y = 12 4. 7x - 2y = 31

We can use different methods such as substitution, elimination, or matrix operations. Let's solve it using the substitution method.

Substitution Method

Step 1: Solve equation 3 for y: - 2x + y = 12 - Subtract 2x from both sides: y = 12 - 2x

Step 2: Substitute the value of y from equation 3 into equations 1, 2, and 4: - Equation 1: 5x - 3(12 - 2x) = 0 - Equation 2: 3x - 4(12 - 2x) = 29 - Equation 4: 7x - 2(12 - 2x) = 31

Step 3: Simplify and solve the resulting equations: - Equation 1: 5x - 36 + 6x = 0 - Combine like terms: 11x - 36 = 0 - Add 36 to both sides: 11x = 36 - Divide by 11: x = 36/11

- Equation 2: 3x - 48 + 8x = 29 - Combine like terms: 11x - 48 = 29 - Add 48 to both sides: 11x = 77 - Divide by 11: x = 77/11

- Equation 4: 7x - 24 + 4x = 31 - Combine like terms: 11x - 24 = 31 - Add 24 to both sides: 11x = 55 - Divide by 11: x = 55/11

Step 4: Substitute the values of x back into equation 3 to solve for y: - Equation 3: 2x + y = 12 - Substitute x = 36/11: 2(36/11) + y = 12 - Simplify: 72/11 + y = 12 - Subtract 72/11 from both sides: y = 12 - 72/11

Therefore, the solution to the system of equations is: - x = 36/11 - y = 12 - 72/11

Let's calculate the values of x and y: - x = 36/11 ≈ 3.27 - y = 12 - 72/11 ≈ -0.18

So, the approximate solution to the system of equations is: - x ≈ 3.27 - y ≈ -0.18

Please note that these values are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.