Question

2x-6(x+3y)=45-3y\\ 6(5x - 7y) =126+10x

Answer 1

Ответ:

(0; -3)

Пошаговое объяснение:

2x-6 (x+3y) = 45-3y

6 (5x-7y) = 126+10x;

2 х-6 х-18 у=45-3 у

30 х-42 у=126+10 х;

2 х-6 х-18 у-45+3 у=0

30 х-42 у-126-10 х=0;

-4 х-15 у-45=0

20 х-42 у-126=0;

х = (42 у+126) / 20

-4 х-15 у-45=0;

х = (42 у+126) / 20

-4 ((42 у+126) / 20) - 15 у-45=0;

х = (42 у+126) / 20

-4 (2,1 у+6,3) - 15 у-45=0;

х = (42 у+126) / 20

-8,4 у-25,2-15 у-45=0;

х = (42 у+126) / 20

-23,4 у=70,2;

у=-3

х = (42 у+126) / 20;

у=-3

х = (42 * (-3) + 126) / 20;

у=-3

х = (-126+126) / 20;

у=-3

х=0.

Answer 2

To solve the system of equations:

1. 2x - 6(x + 3y) = 45 - 3y
2. 6(5x - 7y) = 126 + 10x

Let's simplify each equation step by step.

1. Distribute the -6 in the first equation: 2x - 6x - 18y = 45 - 3y

Combine like terms: -4x - 18y = 45 - 3y

2. Distribute the 6 in the second equation: 30x - 42y = 126 + 10x

Combine like terms: 30x - 10x - 42y = 126

Simplify further: 20x - 42y = 126

Now, we have a system of equations: -4x - 18y = 45 - 3y 20x - 42y = 126

To solve this system, we can use the method of elimination. Multiply the first equation by 2 to make the coefficients of x in both equations equal:

-8x - 36y = 90 - 6y 20x - 42y = 126

Now, add the two equations together to eliminate x:

(-8x + 20x) + (-36y - 42y) = (90 - 6y) + 126

Simplifying further: 12x - 78y = 216

Now, we have a new equation: 12x - 78y = 216

Let's solve this equation for x: 12x = 78y + 216 x = (78y + 216) / 12 x = 6.5y + 18 (equation A)

Now, substitute the value of x in equation A into either of the original equations. Let's use the first equation:

-4(6.5y + 18) - 18y = 45 - 3y

Simplify further: -26y - 72 - 18y = 45 - 3y

Combine like terms: -44y - 72 = 45 - 3y

Add 3y to both sides: -44y + 3y - 72 = 45 - 3y + 3y

Simplify further: -41y - 72 = 45

Add 72 to both sides: -41y - 72 + 72 = 45 + 72

Simplify further: -41y = 117

Divide both sides by -41: y = 117 / -41 y = -3

Now, substitute the value of y back into equation A to find x: x = 6.5y + 18 x = 6.5(-3) + 18 x = -19.5 + 18 x = -1.5

Therefore, the solution to the system of equations is x = -1.5 and y = -3.