EXPLANATION
Given the system of equations:
(1) x = 6y - 2
(2) 2x + 5y = 47
Substituting (1) in (2):
(2) 2(6y - 2) + 5y = 47
Applying the distributive property:
12y - 4 + 5y = 47
Adding like terms:
17y - 4 = 47
Adding +4 to both sides:
17y = 47 + 4
Adding numbers:
17y = 51
Dividing both sides by 17:
y = 51/17
Simplifying:
y = 3
Replacing y=3 in (1):
x = 6(3) - 2
Multiplying numbers:
x = 18 - 2
Subtracting numbers:
x = 16
The solutions to the system of equations are:
(x,y)=(16,3)