Question

X – 4y=-42, 9x+8y=62.​

Answer 1

Ответ:

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В данном случае, систему уравнений проще решить методом подстановки переменной из одного уравнения в другое. Из первого уравнения выразим $x$ и подставим его во второе уравнения системы. Далее упрощаем второе уравнение до нахождения $y$:

$\left \{ {{x=4*y-42} \atop {9*x+8*y=62}} \right. \\\left \{ {{x=4*y-42} \atop {9*(4*y-42)+8*y=62}} \right. \\\left \{ {{x=4*y-42} \atop {36*y-378+8*y=62}} \right.$

$\left \{ {{x=4*y-42} \atop {36*y-378+8*y=62}} \right. \\\left \{ {{x=4*y-42} \atop {44*y=62+378}} \right. \\\left \{ {{x=4*y-42} \atop {44*y=62+378}} \right. \\\left \{ {{x=4*y-42} \atop {44*y=440}} \right.\\\left \{ {{x=4*y-42} \atop {y=\frac{440}{44}}} \right.\\\left \{ {{x=4*y-42} \atop {y=10}} \right.$

Получили, что $y=10$, тогда, возвращаясь в первое уравнение системы находим $x$:

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Answer 2

To solve this system of linear equations:

1. X - 4y = -42
2. 9x + 8y = 62

You can use the method of either substitution or elimination. I'll demonstrate the elimination method.

First, you want to eliminate one of the variables (either x or y) from one of the equations by manipulating the equations. Let's eliminate y from the first equation by multiplying both sides of the equation by 8 to match the coefficients of y in both equations:

1. 8(x - 4y) = 8(-42)

This simplifies to:

1. 8x - 32y = -336

Now you have the following two equations:

1. 8x - 32y = -336
2. 9x + 8y = 62

Next, you can add the two equations together to eliminate y:

(8x - 32y) + (9x + 8y) = -336 + 62

This simplifies to:

17x - 24y = -274

Now, you have a new equation:

3. 17x - 24y = -274

You now have a system of two equations with two variables:

2. 9x + 8y = 62
3. 17x - 24y = -274

Now, you can solve this system of equations simultaneously. One way to do this is to multiply equation (2) by 3 and equation (3) by 2 to make the coefficients of y in both equations cancel each other when added:

Multiply equation (2) by 3:

6. 27x + 24y = 186

Multiply equation (3) by 2:

7. 34x - 48y = -548

Now, you can add equation (6) and equation (7) to eliminate y:

(27x + 24y) + (34x - 48y) = 186 - 548

This simplifies to:

61x = -362

Now, solve for x:

x = -362 / 61 x = -6

Now that you have the value of x, you can substitute it into either equation (2) or equation (3) to solve for y. I'll use equation (2):

9x + 8y = 62 9(-6) + 8y = 62 -54 + 8y = 62

Add 54 to both sides:

8y = 62 + 54 8y = 116

Now, solve for y:

y = 116 / 8 y = 14.5

So, the solution to the system of equations is:

x = -6 y = 14.5