Question

5а+7в=-6 6а+в=16 решите способом сложения

Answer 1

5a+7b=-6 |•(-1) -5a-7b=6
6a+b=16 |•(7) 42a+7b=112

37a=118 6•3.2+b=16
a=118:37 19.2+b=16
a=3.2 b=16-19.2
b=-3.2
В:(3.2;-3.2)

Answer 2

To solve the system of equations using the method of addition (also known as the method of elimination), we'll eliminate one variable by adding the two equations. Here's the system of equations:

1. 5а + 7в = -6 ......(Equation 1)
2. 6а + в = 16 ......(Equation 2)

Step 1: Multiply Equation 1 by 6 and Equation 2 by 5 to make the coefficients of 'а' in both equations the same:

Multiply Equation 1 by 6: 6(5а + 7в) = 6(-6) 30а + 42в = -36

Multiply Equation 2 by 5: 5(6а + в) = 5(16) 30а + 5в = 80

The equations become: 3. 30а + 42в = -36 ......(Equation 3)

4. 30а + 5в = 80 ......(Equation 4)

Step 2: Now, we'll subtract Equation 4 from Equation 3 to eliminate the 'а' variable:

(Equation 3) - (Equation 4): (30а + 42в) - (30а + 5в) = -36 - 80 30а - 30а + 42в - 5в = -116 37в = -116

Step 3: Solve for 'в':

в = -116 / 37 в = -3.1351 (approximately)

Step 4: Substitute the value of 'в' into either Equation 1 or Equation 2 to solve for 'а'. Let's use Equation 1:

5а + 7(-3.1351) = -6

Step 5: Solve for 'а':

5а - 21.9455 = -6

5а = -6 + 21.9455

5а = 15.9455

а = 15.9455 / 5

а = 3.1891 (approximately)

So the solution to the system of equations is: а ≈ 3.1891 в ≈ -3.1351