Question

Різниця двох чисел дорівнює 21. Відомо, що друге число у 4 рази більше за перше. Яка із наведених систем рівнянь вiдповiдає цiй умові, якщо більше число позначили через x, а менше - через у? 1) {x - y = 21; x = 4y2( {x - y = 21; y = 4x3) {y - x = 21; x = 4y4) {y - x = 21; y = 4xПОМОГИТЕ ПЖ​ Посмотреть ответы Участник Знаний Участник Знаний Відповідь:Пояснення:фото допоможіть будь ласка на останню завданні iramazurk iramazurk Объяснение:Большее число = хМеньшее число = у у - х = 21х = 4уОтвет: 3)1)у - х = 21у - 4у = 21-3у = 21у = -72)х = 4у х = 4 * (-7) х = -28 Помоги с ище одним решением в профиле посмотри новое

Answer 1

Problem Analysis

We are given that the difference between two numbers is 21, and the second number is 4 times greater than the first number. We need to determine which of the given systems of equations satisfies these conditions.

Solution

Let's analyze each system of equations to see which one satisfies the given conditions.

1) {x - y = 21; x = 4y^2 2) {x - y = 21; y = 4x^3 3) {y - x = 21; x = 4y^4 4) {y - x = 21; y = 4x

Let's start with the first system of equations: 1) {x - y = 21; x = 4y^2

If we substitute the value of x from the second equation into the first equation, we get: 4y^2 - y = 21

Simplifying this equation, we have: 4y^2 - y - 21 = 0

This is a quadratic equation in terms of y. We can solve it using factoring, completing the square, or the quadratic formula. However, let's check the other systems of equations before solving this equation.

Now let's move on to the second system of equations: 2) {x - y = 21; y = 4x^3

If we substitute the value of y from the second equation into the first equation, we get: x - 4x^3 = 21

Simplifying this equation, we have: 4x^3 - x - 21 = 0

This is also a cubic equation in terms of x. We can solve it using factoring, synthetic division, or numerical methods. However, let's check the remaining systems of equations before solving this equation.

Next, let's consider the third system of equations: 3) {y - x = 21; x = 4y^4

If we substitute the value of x from the second equation into the first equation, we get: y - 4y^4 = 21

Simplifying this equation, we have: 4y^4 - y + 21 = 0

This is a quartic equation in terms of y. We can solve it using factoring, synthetic division, or numerical methods. However, let's check the last system of equations before solving this equation.

Finally, let's analyze the fourth system of equations: 4) {y - x = 21; y = 4x

If we substitute the value of y from the second equation into the first equation, we get: 4x - x = 21

Simplifying this equation, we have: 3x = 21

Dividing both sides by 3, we find: x = 7

Now, substituting this value of x into the second equation, we have: y = 4(7) = 28

So, the values of x and y that satisfy the fourth system of equations are x = 7 and y = 28.

To summarize, the fourth system of equations {y - x = 21; y = 4x satisfies the given conditions.

Answer: The fourth system of equations {y - x = 21; y = 4x satisfies the given conditions.

Please note that the solutions to the quadratic, cubic, and quartic equations in the other systems of equations were not calculated, as they were not necessary to determine the correct system of equations.