Question

{4(x+5)+2(y-6)=1-3y {3(y+4)+6x-7=2(1+2x) Решите систему уравнений заранее благодарен...

Answer 1

{4x+20+2y-12=1-3y

{3y+12+6x-7=2+4x

 

{4x+5y=-7

{3y+2x=-10

 

{4x=-20-6y

{4x=-7-5y

 

{-20-6y=-7-5y

{-13=y

{x=14.5

 

Answer 2

Solving the System of Equations

To solve the system of equations 4(x+5) + 2(y-6) = 1 - 3y and 3(y+4) + 6x - 7 = 2(1+2x), we can use the method of substitution or elimination. Let's use the elimination method.

First, let's simplify the equations:

Equation 1: 4x + 20 + 2y - 12 = 1 - 3y Simplifying Equation 1: 4x + 2y + 8 = 1 - 3y Rearranging Equation 1: 4x + 2y + 3y = 1 - 8 Simplifying Equation 1 further: 4x + 5y = -7 Equation 2: 3y + 12 + 6x - 7 = 2 + 4x Simplifying Equation 2: 6x + 3y + 5 = 2 + 4x Rearranging Equation 2: 6x + 3y - 4x = 2 - 5 Simplifying Equation 2 further: 2x + 3y = -3 Now we have a system of equations:

Equation 3: 4x + 5y = -7 Equation 4: 2x + 3y = -3

To solve this system, we can multiply Equation 4 by 2 and Equation 3 by 3 to eliminate the variable x:

Multiplying Equation 4 by 2: 4x + 6y = -6 Multiplying Equation 3 by 3: 12x + 15y = -21

Now we have a new system of equations:

Equation 5: 4x + 6y = -6 Equation 6: 12x + 15y = -21

Subtracting Equation 5 from Equation 6, we can eliminate the variable x:

Equation 6 - Equation 5: (12x + 15y) - (4x + 6y) = (-21) - (-6) Simplifying: 8x + 9y = -15 Now we have a new equation:

Equation 7: 8x + 9y = -15

To solve for x and y, we can solve the system of equations formed by Equation 7 and Equation 4:

Equation 7: 8x + 9y = -15 Equation 4: 2x + 3y = -3

We can solve this system using the elimination method. Multiplying Equation 4 by 4 and Equation 7 by 2, we can eliminate the variable y:

Multiplying Equation 4 by 4: 8x + 12y = -12 Multiplying Equation 7 by 2: 16x + 18y = -30

Now we have a new system of equations:

Equation 8: 8x + 12y = -12 Equation 9: 16x + 18y = -30

Subtracting Equation 8 from Equation 9, we can eliminate the variable x:

Equation 9 - Equation 8: (16x + 18y) - (8x + 12y) = (-30) - (-12) Simplifying: 8x + 6y = -18 Now we have a new equation:

Equation 10: 8x + 6y = -18

To solve for x and y, we can solve the system of equations formed by Equation 10 and Equation 7:

Equation 10: 8x + 6y = -18 Equation 7: 8x + 9y = -15

We can solve this system using the elimination method. Multiplying Equation 7 by 2 and Equation 10 by 3, we can eliminate the variable x:

Multiplying Equation 7 by 2: 16x + 18y = -30 Multiplying Equation 10 by 3: 24x + 18y = -54

Now we have a new system of equations:

Equation 11: 16x + 18y = -30 Equation 12: 24x + 18y = -54

Subtracting Equation 11 from Equation 12, we can eliminate the variable y:

Equation 12 - Equation 11: (24x + 18y) - (16x + 18y) = (-54) - (-30) Simplifying: 8x = -24 Solving for x: x = -3 Now that we have the value of x, we can substitute it back into Equation 7 to solve for y:

Equation 7: 8x + 9y = -15 Substituting x = -3: 8(-3) + 9y = -15 Simplifying: -24 + 9y = -15 Solving for y: 9y = -15 + 24 Simplifying further: 9y = 9 Solving for y: y = 1 Therefore, the solution to the system of equations is x = -3 and y = 1.