Solve by the elimination method.

6x−5y=
47
5x+7y=
−39
.
.
.
Question content area right
Part 1
What is the solution set of the​ system? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your answer.
A.
The solution is enter your response here .
​(Simplify your answer. Type an ordered​ pair.)
B.
There are infinitely many solutions. The solution set is x,enter your response here.
​(Simplify your answer. Type an expression in terms of​ x.)
C.
The solution is the empty set.

1 answer

To solve by the elimination method, we need to eliminate one variable by adding the equations together or subtracting one equation from the other. Let's multiply the first equation by 5 and the second equation by 6 to make the coefficients of y the same:

30x - 25y = 235
30x + 42y = -234

Now, we can subtract these two equations to eliminate the x variable:

(30x - 25y) - (30x + 42y) = 235 - (-234)
-67y = 469
y = -7

Substituting this value of y into one of the original equations, we can solve for x:

6x - 5(-7) = 47
6x + 35 = 47
6x = 12
x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -7).

The correct choice is A. The solution is (2, -7).