What is the best approximation of the solution to the system to the nearest valus 2x-3y=-6 and x+2y=8

Given:

2x - 3y = - 6 ⇒ identified as 1st equation

x + 2y = 8 ⇒ identified as 2nd equation

Let us first get the value of x using the 2nd equation.

x + 2y = 8

x = 8 - 2y

Substitute x in the 1st equation with its value and find the value of y.

2x - 3y = - 6

2 (8-2y) - 3y = - 6

16 - 4y - 3y = - 6

-4y - 3y = - 6 - 16

-7y = - 22

y = - 22/-7

y = 22/7 simplified to 3 1/7

Substitute the value of y in the 2nd equation.

x = 8 - 2y

x = 8 - 2 (22/7)

x = 8 - 44/7

x = (8 * 7/7) - 44/7

x = 56/7 - 44/7

x = (56-44) / 7

x = 12/7 simplified to 1 5/7

To check: x = 12/7 and y = 22/7 * we need to use the improper fractions.

2x - 3y = - 6

2 (12/7) - 3 (22/7) = - 6

24/7 - 66/7 = - 6

(24-66) / 7 = - 6

-42/7 = - 6

-6 = - 6

x + 2y = 8

12/7 + 2 (22/7) = 8

12/7 + 44/7 = 8

(12+44) / 7 = 8

56/7 = 8

8 = 8