Question

5x+2y=15,8x+Зу = 20​

Answer 1

Ответ:

1) 5х+2у-15=0

2)8х+3у-20=0

Answer 2

Ответ:

1) 5x+2y-15=0

2) 8x+3y-20=0

Answer 3

To solve the system of equations:

5x + 2y = 15 ...(Equation 1) 8x + 3y = 20 ...(Equation 2)

There are multiple ways to solve this system, such as substitution, elimination, or using matrices. Here, I will show you how to solve it using the elimination method:

Step 1: Multiply Equation 1 by 4 and Equation 2 by 5 to make the coefficients of 'y' in both equations the same. This will allow us to eliminate 'y' when we subtract the equations.

4(5x + 2y) = 4(15) ...(Multiply Equation 1 by 4) 5(8x + 3y) = 5(20) ...(Multiply Equation 2 by 5)

Simplifying these equations, we get:

20x + 8y = 60 ...(Equation 3) 40x + 15y = 100 ...(Equation 4)

Step 2: Now, subtract Equation 3 from Equation 4 to eliminate 'x':

(40x + 15y) - (20x + 8y) = 100 - 60

Simplifying this equation, we get:

20x + 7y = 40 ...(Equation 5)

Step 3: Now we have two equations:

20x + 7y = 40 ...(Equation 5) 8x + 3y = 20 ...(Equation 2)

We can solve this system using either substitution or elimination method. I will use the elimination method again to eliminate 'x'.

Step 4: Multiply Equation 5 by 4 and Equation 2 by 5 to make the coefficients of 'x' in both equations the same:

4(20x + 7y) = 4(40) ...(Multiply Equation 5 by 4) 5(8x + 3y) = 5(20) ...(Multiply Equation 2 by 5)

Simplifying these equations, we get:

80x + 28y = 160 ...(Equation 6) 40x + 15y = 100 ...(Equation 4)

Step 5: Subtract Equation 4 from Equation 6 to eliminate 'y':

(80x + 28y) - (40x + 15y) = 160 - 100

Simplifying this equation, we get:

40x + 13y = 60 ...(Equation 7)

Step 6: Now we have two equations:

40x + 13y = 60 ...(Equation 7) 40x + 15y = 100 ...(Equation 4)

Step 7: Subtract Equation 7 from Equation 4 to eliminate 'x':

(40x + 15y) - (40x + 13y) = 100 - 60

Simplifying this equation, we get:

2y = 40

Dividing both sides by 2, we find:

y = 20

Step 8: Now that we have the value of 'y', we can substitute it back into Equation 4 to find 'x':

40x + 15(20) = 100

Simplifying this equation, we get:

40x + 300 = 100

Subtracting 300 from both sides, we get:

40x = -200

Dividing both sides by 40, we find:

x = -5

Therefore, the solution to the system of equations is x = -5 and y = 20.