Question

Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x, y) if there is one, unique solution. Enter All​ if there are infinitely many solutions and enter None​ if there are no solutions.

6x−5y=61
2x+6y=−18

Answer 1

The first person who answered is correct!!!!

Answer 2

Answer: The solution to the system of equations is (x, y) = (3, -79/14).

Step-by-step explanation:

2(6x - 5y) = 2(61)
-3(2x + 6y) = -3(-18)

This simplifies to:
12x - 10y = 122
-6x - 18y = 54

Now, we can add the two equations together to eliminate x:
(12x - 10y) + (-6x - 18y) = 122 + 54
6x - 28y = 176

Simplifying more:
6x - 28y = 176

Now solve for y:
-28y = -6x + 176
y = (6/28)x - 176/28
y = (3/14)x - 44/7

Now,m substitute this value of y back into one of the original equations to solve for x. Using the first equation:
6x - 5((3/14)x - 44/7) = 61
6x - (15/14)x + 220/7 = 61
(84/14)x - (15/14)x = 61 - 220/7
(69/14)x = 61 - 220/7
(69/14)x = (61*7 - 220)/7
(69/14)x = (427 - 220)/7
(69/14)x = 207/7
x = (207/7)(14/69)
x = 3

Now that we have the value of x, we can substitute it back into the equation for y:
y = (3/14)(3) - 44/7
y = 9/14 - 44/7
y = (9 - 88)/14
y = -79/14