Question

2(х-3)+у=-4 3(у-1)+2х=3

Answer 1

Ответом будет (0;2), решено методом сложения

Answer 2

To solve the system of equations:

1. 2(x - 3) + y = -4
2. 3(y - 1) + 2x = 3

We can use the method of substitution or elimination. I'll demonstrate the elimination method here:

Step 1: Multiply the first equation by 3 and the second equation by 2 to eliminate the coefficients of x:

1. 3 * [2(x - 3) + y] = 3 * (-4)
2. 2 * [3(y - 1) + 2x] = 2 * 3

This simplifies the system to:

1. 6(x - 3) + 3y = -12
2. 6(y - 1) + 4x = 6

Step 2: Distribute and rearrange the equations:

1. 6x - 18 + 3y = -12
2. 4x + 6y - 6 = 6

Step 3: Now, let's put both equations in standard form (ax + by = c):

1. 6x + 3y = -12 + 18 6x + 3y = 6 ... (Equation 1')

2. 4x + 6y = 6 + 6 4x + 6y = 12 ... (Equation 2')

Step 4: Multiply Equation 1' by 2 and Equation 2' by -3 to make the coefficients of x in both equations equal:

1. 2 * (6x + 3y) = 2 * 6 12x + 6y = 12 ... (Equation 3')

2. -3 * (4x + 6y) = -3 * 12 -12x - 18y = -36 ... (Equation 4')

Step 5: Add Equation 3' and Equation 4' to eliminate x:

(12x + 6y) + (-12x - 18y) = 12 + (-36)

The x terms cancel out:

-12y = -24

Step 6: Solve for y:

y = (-24) / (-12) y = 2

Step 7: Substitute the value of y (which is 2) into either Equation 1' or Equation 2' to solve for x. Let's use Equation 1':

6x + 3(2) = 6

Step 8: Solve for x:

6x + 6 = 6 6x = 6 - 6 6x = 0

x = 0

Step 9: Now that we have found the values of x and y, we can verify by substituting them back into either of the original equations. Let's use the first equation:

2(x - 3) + y = -4 2(0 - 3) + 2 = -4 2(-3) + 2 = -4 -6 + 2 = -4 -4 = -4

The equation is true. So, the solution to the system of equations is x = 0 and y = 2.