Question

{x+4y/9 - x-2y/3 = 0 {x+7y/4 + x+y/6 = 4 Смотреть ответ snow99 snow99 Ответ: (5; 1)

Answer 1

To find the solution to the system of equations, let's start by writing the equations in a clearer format:

1. Equation 1: (x + 4y)/9 - (x - 2y)/3 = 0
2. Equation 2: (x + 7y)/4 + (x + y)/6 = 4

Now, let's solve the system step-by-step:

Step 1: Clear the fractions to simplify the equations.

For Equation 1, the common denominator of 9 and 3 is 9: (3*(x + 4y) - 9*(x - 2y))/9 = 0 (3x + 12y - 9x + 18y)/9 = 0 (-6x + 30y)/9 = 0 (-2x + 10y)/3 = 0

For Equation 2, the common denominator of 4 and 6 is 12: (6*(x + 7y) + 4*(x + y))/12 = 4 (6x + 42y + 4x + 4y)/12 = 4 (10x + 46y)/12 = 4 (5x + 23y)/6 = 4

Step 2: Set each equation equal to zero and isolate one variable in each equation.

Equation 1: (-2x + 10y)/3 = 0 -2x + 10y = 0 -2x = -10y x = (10y)/2 x = 5y

Equation 2: (5x + 23y)/6 = 4 5x + 23y = 24 5x = 24 - 23y x = (24 - 23y)/5

Step 3: Equate the two expressions for x and solve for y.

Since both expressions are equal to x, we can set them equal to each other: 5y = (24 - 23y)/5

Step 4: Solve for y.

To solve for y, let's get rid of the fraction: 5y = 24 - 23y 5y + 23y = 24 28y = 24 y = 24/28 y = 6/7

Step 5: Find the value of x.

Now that we have the value of y, we can find x using either of the equations we found earlier for x: x = 5y x = 5 * (6/7) x = 30/7

So, the solution to the system of equations is x = 30/7 and y = 6/7, which can be approximated to x ≈ 4.29 and y ≈ 0.86.

However, this solution does not match the answer you provided (5; 1). There might be an error in the original system of equations or the answer. Please double-check the equations or clarify the context if there's any discrepancy.